There are 42 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 6 min. (Give answers accurate to 3 decimal places.)
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?
1
(b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?
2
Answers
Answer:
A) 0.99413
B) 0.00022
Step-by-step explanation:
A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:
Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes
Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:
μ = n*μ_s ample = 42 × 5 = 210 minutes
While the standard deviation for the population would be:
σ = √nσ_sample = √(42 × 6) = 15.8745 minutes
To find the z-score, we will use the formula;
z = (x - μ)/σ
Thus;
z = (250 - 210)/15.8745
z = 2.52
From the z-distribution table attached, we have;
P(Z < 2.52) ≈ 0.99413
B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.
Thus, total time is now 250 + 10 = 260 minutes
Similar to the z-formula in A above, we have;
z = (260 - 210)/15.8745
z = 3.15
P(Z > 3.15) = 0.00022
Related Questions
What is the quotient matches 22/33 divided by 6/9
Answers
Hey there! I'm happy to help!
When you divide fractions, you are technically multiplying by the reciprocal, which is the numerator and denominator flipped. This means that 22/33 divided by 6/9 is equal to 22/33 multiplied by 9/6.
If we multiply these together, we get an answer of 1.
I hope that this helps! Have a wonderful day!
The calculated division of the numbers 22/33 divided by 6/9 is 1
How to calculate the division of the numbersFrom the question, we have the following parameters that can be used in our computation:
22/33 divided by 6/9
When represented as an equation, we have
22/33 divided by 6/9 = 22/33 ÷ 6/9
Represent as a product expression
So, we have
22/33 divided by 6/9 = 22/33 * 9/6
So, we have the following result
22/33 divided by 6/9 = 1
Using the above as a guide, we have the following:
the result is 1
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A compressive uniform stress distributed on a rectangular areas of sides. located on the two opposite vertical/radial faces of step. If Force = 1.87kN and stress = 0.987MPa calculate the h * t in m^2
Answers
Answer:
Area = 0.019 m²
Step-by-step explanation:
stess = applied Force over Area
since stress = 0.987 MPa
and the force = 1.87 Kn
then Area = h * t
Q = F / (h * t)
0.987 mPa = 1.87 kN / (h* t)
since h * t = Area then 1.87 / 0.987
Area = 1.89 x 0.01 =
Area = 0.019 m²
Sally can paint a room in 9 hours while it takes Steve 6 hours to paint the same room. How long would it take them to paint the room if they worked together?
Answers
Answer:
3.6
Step-by-step explanation:
1/9+1/6
1/3^2+1/2x3=1/x
2+3/3^2x2=1/x
5/3^2x2=1/x
x.5=18
5x=18
5x/5= 18/5
x=18/5
x=3.6
To paint the room if they worked together in 4 hours 14 min.
To find time if they work together.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers.An arithmetic sequence is a sequence where the difference between each successive pair of terms is the same. The explicit rule to write the formula for any arithmetic sequence is this:
an = a1 + d (n - 1).
Given that:
(1 room/Sally's time) + (1 room/Steve's time) = (1 room)/(time working together)
1/9+1/6+=+1/x
Multiply both sides by 54x
6x+9x=54
15x=54
x=3.6hours
Working together, they can paint the room in 3 hours 6 min.
So, to paint the room if they worked together in 3 hours 6 min.
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I NEED HELP ASAP choose one of the multiple choice
Answers
Answer:
B. Square both sides of the equation.
Step-by-step explanation:
You cannot do anything to the equation unless you square both sides to eliminate the square root on the left (squaring each individual term of the equation does not help; you need to square the entire square root to eliminate it).
Hope this helps!
Which confidence level will yield the interval that we are most confident in containing the actual value of the population parameter?
a. 99.2%
b. 99.5%
c. Our confidence in whether an interval actually contains the parameter is not affected by the choice of confidence level.
d. 99.9%
Answers
Answer:
The confidence level that will yield the interval that we are most confident in containing the actual value of the population parameter is (d) 99.9%
Step-by-step explanation:
the confidence level can be explained simply as a range of values that are well defined and that they contain a specified probability that the value of a parameter lies within the confidence level.
for example when we compare a 99.2% confidence level and 99.9% confidence level, when we have a narrow confidence interval 99.2 (say) this implies that there is a smaller chance of obtaining an observation within that interval, so therefore, our accuracy is higher. Also a 99.2% confidence interval is narrower than a 99.9% confidence interval which is wider. The 99.9% confidence interval is more accurate than the 99.2%.
so that is why we concluded that the most confidence level is 99.9%.
Answer:
Which confidence interval is most likely to contain the population parameter?
✔ between 7.0 and 9.0 hours of sleep
Step-by-step explanation:
Mitch mixes 5 parts white paint to 9 parts blue paint. If he has 4 qt of white paint, how much blue paint would he need?
He would need
qt of blue paint
Answers
Answer:
7.2 qt
Step-by-step explanation:
1. Determine how much blue paint is needed in comparison to white paint
9 ÷ 5 = 1.8
For every 1 part of white paint, 1.8 times that amount of blue paint is needed.
2. Multiply the 4 qt of white paint by 1.8
4 · 1.8 = 7.2
The number of blue paints Mitch will need given the proportion of white and blue paints is 7.2qt
Given:
Blue paints = 9
White paints = 5
Ratio of blue paints to white paints = 9 : 5
If Mitch has 4 qt of white paintNumber of blue paints needed is xRatio of blue paints to white paints = x : 4
Equate the ratio9 : 5 = x : 4
9/5 = x/4
cross product
9 × 4 = 5 × x
36 = 5x
x = 36/5
x = 7.2 qt
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Degree Of Length Degree Of Width Degree Of Height Degree Of Volume
Answers
Answer: length = 1, width = 1, height = 3, volume = 5
Step-by-step explanation:
Degree is the biggest exponent for the variables in the expression
Length = 4x - 1. The exponent for x is 1 --> degree = 1
Width = x The exponent for x is 1 --> degree = 1
Height = x³ The exponent for x³ is 3 --> degree = 3
Volume = 4x⁵ - x⁴. The biggest exponent for x is 5 --> degree = 5
Answer:
- First answer: 1
- Second answer: 1
- Third answer: 3
- Last answer: 5
Step-by-step explanation:
Correct on E2020
A physics class has students. Of these, students are physics majors and students are female. Of the physics majors, are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is nothing.\
Answers
Answer:
The probability that a randomly selected student is female or a physics major is 0.65.
Step-by-step explanation:
Note: This question is not complete. A complete is therefore provided before answering the question as follows:
A physics class has 40 students. Of these, 14 students are physics majors and 18 students are female. Of the physics majors, six are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is_______.
The Step-by-step explanation is therefore provided now as follows:
The probability that a randomly selected student is female or a physics major can be calculated using the following formula:
P(PM or F) = P(PM) + P(F) - P(PMF)
Where;
P(PM or F) = Probability of student selected is Physics Major or Female = ?
P(PM) = Probability of student selected is Physics Major = Number of Physics Major / Total number of students in the Physics class = 14 / 40 = 0.35
P(F) = Probability of student selected is Female = Number of female students in the Physics class / Total number students in the Physics class = 18 / 40 = 0.45
P(PMF) = Probability of student selected is Physics Major and Female = Number Physics Major that female in the Physics class / Total number students in the Physics class = 6 / 40 = 0.15
Substituting the values into equation (1), we have:
P(PM or F) = 0.35 + 0.45 - 0.15 = 0.65
Therefore, the probability that a randomly selected student is female or a physics major is 0.65.
Answer:
what is the physics question
Step-by-step explanation:
Which relation is a function?
Answers
Answer:
D
Step-by-step explanation:
a function is a relation of two sets that associates to every number of the first set only one number of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers.
Answer:
D. the quadratic equation
Step-by-step explanation:
This is because in a function, there can not be multiple solutions for one x value. Each of the graphs display points in which the answer to x is multiple values of y, which is not a characteristic of a function.
You can see this by doing a vertical line test. Place and guide your pencil or any straight edge along the beginning of a graph to the end. If the line crosses x at two or more points, the graph is not a function. The quadratic equation is the only one that is a function because as your pencil moves along, you will see that each point has its own x value and nothing overlaps.
Which statement is true about figures ABC D & ABCD
Answers
Answer:
it's option b that is the right answer
Part of the proceeds from a garage sale was $440 worth of $10 and $20 bills. If there were 2 more $10 bills than $20 bills, find the number of each denomination.
Answers
Hey there! I'm happy to help!
Let's set this up a system of equations where x represents the number of 10 dollar bills and y represents the number of 20 dollar bills.
10x+20y=440
x=y+2
We see that x has a value of y+2, so we can replace the x in the first equation with y+2 so we can solve for y.
10(y+2)+20y=440
We use distributive property to undo the parentheses.
10y+20+20y=440
We combine like terms.
30y+20=440
We subtract 20 from both sides.
30y=420
y=14
Since there are 2 more $10 bills, there would be 16 of those.
Therefore, there are 16 $10 bills and 14 $20 bills.
Have a wonderful day! :D
What is the radius of a circle given by the equation x2 + y2 – 2x + 8y – 47= 0? radius = units
Answers
Answer:
8 units
Step-by-step explanation:
We need to rewrite an equation in the standard for a circle form.
r is radius.
(x−h)²+(y−k)²= r²
x² + y² – 2x + 8y – 47= 0
x² - 2x + y² + 8y - 47 = 0
x² - 2*x *1+ 1 ²- 1² + y² + 2*4*y + 4² - 4² - 47 = 0
(x - 1)² + (y + 4)² - 1 - 16 -47 =0
(x - 1)² + (y + 4)² - 64=0
(x - 1)² + (y + 4)² = 8²
Radius is 8.
The radius of the circle is 8 units
What is radius?The radius of a circle is a line drawn from the center to the circumference of the circle
The equation of the circle is given as;
[tex]x^2 + y^2 - 2x + 8y - 47 = 0[/tex]
Rewrite the equation as:
[tex]x^2 - 2x + y^2 + 8y = 47[/tex]
Next, we rewrite the equation in the standard form
So, we have:
x^2 - 2x + 1^2 - 1^2 + y^2 + 8y + 4^2 - 4^2 = 47
Evaluate the exponents
x^2 - 2x + 1 - 1 + y^2 + 8y + 16 - 16 = 47
Rewrite the equation as follows:
x^2 - 2x + 1 + y^2 + 8y + 16 = 47 + 1 + 16
Express as perfect squares
(x - 1)² + (y + 4)² = 64
(x - 1)² + (y + 4)² = 8^2
The radius of the circle is calculated as:
r^2 = 8^2
By comparison, we have:
r = 8
Hence, the radius of the circle is 8 units
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PLS PLSPLS HELPPP------
Answers
Answer:
Total Area = [tex]104+16\,\sqrt{13}[/tex]
Step-by-step explanation:
If T.A. stands for Total Area, then we need to add the area of two equal right angle triangles of base 6' and height 4', which give : 2 * (6' * 4'/2) = 24 square feet. tothe area of three rectangles (the lateral faces of this triangular base prism):
[tex](8')*(4')+(8')*(6')+(8')*(\sqrt{6^2+4^2})= 32+48+8\,\sqrt{52} =80+8\,*\,2\,\sqrt{13}=80+16\,\sqrt{13}[/tex]
Therefore the total area of the prism is:
[tex]24+80+16\,\sqrt{13} =104+16\,\sqrt{13}[/tex]
A company has five employees on its health insurance plan. Each year, each employee independently has an 80% probability of no hospital admissions. If an employee requires one or more hospital admissions, the number of admissions is modeled by a geometric distribution with a mean of 1.50. The numbers of hospital admissions of different employees are mutually independent. Each hospital admission costs 20,000.
Calculate the probability that the company's total hospital costs in a year are less than 50,000.
Answers
Answer:
the probability that the company's total hospital costs in a year are less than 50,000 = 0.7828
Step-by-step explanation:
From the given information:
the probability that the company's total hospital costs in a year are less than 50,000 will be the sum of the probability of the employees admitted.
If anyone is admitted to the hospital, they have [tex]\dfrac{1}{3}[/tex] probability of making at least one more visit, and a [tex]\dfrac{2}{3}[/tex] probability that this is their last visit.
If zero employee was admitted ;
Then:
Probability = (0.80)⁵
Probability = 0.3277
If one employee is admitted once;
Probability = [tex](0.80)^4 \times (0.20)^1 \times (^5_1) \times (\dfrac{2}{3})[/tex]
Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{2}{3})[/tex]
Probability = 0.2731
If one employee is admitted twice
Probability = [tex](0.80)^3 \times (0.20)^2 \times (^5_2) \times (\dfrac{2}{3})^2[/tex]
Probability = [tex](0.80)^3 \times (0.20)^2 \times (\dfrac{5!}{(5-2)!}) \times (\dfrac{2}{3})^2[/tex]
Probability = 0.1820
If two employees are admitted once
Probability = [tex](0.80)^4\times (0.20)^1 \times (^5_1) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]
Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]
Probability = 0.0910
∴
the probability that the company's total hospital costs in a year are less than 50,000 = 0.3277 + 0.2731 + 0.1820
the probability that the company's total hospital costs in a year are less than 50,000 = 0.7828
Find the common ratio of the following geometric sequence:
11,55, 275, 1375, ....
Answers
Answer:
Hey there!
The common ratio is 5, because you multiply by 5 to get from one term to the next.
Hope this helps :)
Answer:
5
Step-by-step explanation:
To find the common ratio take the second term and divide by the first term
55/11 = 5
The common ratio would be 5
The solutions to the inequality ys-x+1 are shaded on
the graph. Which point is a solution?
(2, 3)
(3,-2)
(2.1)
(-1,3)
Answers
Answer:
the solutions to the inequality ys-x+1 are shaded on the graph. which point is B. (3 ,-2)
John needs to produce a scale diagram of a bedroom using a scale of 1:40. The length of the room is 3.4 metres. What is the length on the diagram? _____ cm
Answers
Answer:
8.5cm
Step-by-step explanation:
convert 3.4metres to cm that is by multiplying by 100
3.4×100=340cm
1rep 40
?rep 340
that is 340/40
=8.5cm
Answer:
8.5 cm
Step-by-step explanation:
Scale = 1:40
Length of the room = 3.4 meters
3.4 meters =3.4 X 100 =340 cm
Since 1 unit on the diagram represents 40 units
The length of the diagram
[tex]=\dfrac{340}{40}\\\\=8.5$ cm[/tex]
The length of the room on the diagram is 8.5 cm.
Determine whether the outcome of the following hypothesis test was a correct decision, a type I error, or a type II error. Claim: "Less than 40% of college students graduate with student loan debt." A hypothesis test of this claim resulted in the decision to reject H0. The actual percentage of college graduates with student loan debt is 45%.
Answers
Answer:
Step-by-step explanation:
The claim: "Less than 40% of college students graduate with student loan debt."
The null hypothesis: more than 40% of college students graduate with student loan debt." p >= 40%
If the actual percentage of college graduates with student loan debt is 45%. The researcher was supposed to fail to reject the null but since he rejected it when it was actually true, it is a type I error.
A type I error occurs when the research rejects the null when it is actually true.
A customer gave her hair dresser a 20% tip, which amounted to $7. What was the price before the tip?
Answers
Answer:
The price before tip was 35
Step-by-step explanation:
Let x = original amount
x * 20% = 7
Change to decimal form
x * .20 = 7
Divide each side by .20
x*.20/.20 = 7/.20
x =35
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the hair colors hair colors of respondents are identified as 100100 for brown hair commabrown hair, 200200 for blond hair commablond hair, 300300 for black hair commablack hair, and 400400 for anything else. The average (mean) is calculated for 503503 respondents and the result is 256.1 .256.1. The data are at the ▼ ordinal interval nominal ratio level of measurement.
Answers
Answer:
Nominal level of measurement
Step-by-step explanation:
The level of measurements used in this study is the nominal level of measurements. The nominal level of measurements involves the use of numbers to help classify the categories in an experiment.
In this case study, values were gotten for each categories which are brown hair, blonde hair, black hair and other hair colors. Thus, the level of measurements used is the nominal level of measurement.
There is something wrong with the calculation because data was gotten for a total of 600 respondents while the mean that was calculated involved only 503 omitting about 97 respondents.
You randomly select an integer from 0 to 24 (inclusively) and then randomly select an integer from 0 to 7 (inclusively). What is the probability of selecting a 5 both times?
Answers
Answer:
1/200
Step-by-step explanation:
There are 24 - 0 + 1 = 25 integers from 0 - 24 (inclusive) and 7 - 0 + 1 = 8 integers from 0 - 7 (inclusive) so there are 25 * 8 = 200 possible outcomes from selecting a random integer from each interval. Of these outcomes, there is only one where you select a 5 both times, so the probability is 1/200.
The probability of selecting a 5 both times is 0.005
Given:
integer from 0 to 24
integer from 0 to 7
Now let determine the probability of selecting a 5 both times
P(getting 5 both times)=?
P(1st time 5)=1/25
P(2nd time 5)=1/8
Hence:
P(getting 5 both times) =(1/25)(×1/8)
P(getting 5 both times)=0.04×0.125
P(getting 5 both times)=0.005
Inconclusion The probability of selecting a 5 both times is 0.005
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there are 80 students in class among them 25 are girls and remaining are boys 10 foreigners and remaining are neplese. If 62.5% of them are nepalese boys, what is the probability of selecting foreign girl?
Answers
Answer:
1/4
Step-by-step explanation:
There are 80 students.
25 are girls and 55 are boys.
10 are foreigners and 70 are Nepalese.
62.5% are Nepalese boys.
This means that the number of Nepalese boys is:
62.5/100 * 80 = 50
There are 50 nepalese boys and so there are 20 nepalese girls.
The probability of selecting a Nepalese girl is therefore:
20 / 80 = 1/4
Write a short statement that expresses a possible function between the given variables. (price of a DVD player, demand f for DVD player)
Answers
Answer:
The relation PriceVSDemand usually is an inverse relationship.
This means that, as the price of the object increases, the demand will decrease.
An inverse relationship is:
D = k/P
Where D is the demand, P is the price and K is a constant that depends on the situation.
Of course this relationship also can be something like:
D = k/P^n
With n ≥ 1.
If n = 1 we have the same as above, and if n > 1, the demand decreases faster as the price increases.
If
2. The first and last term of an AP are 1 and 121 respectively. If the sum of the
series is 671, find a) the number of terms in) in the AP b) the common
difference between them.
Answers
Step-by-step explanation:
since you provided 1st and the last terms
the equation can be nth term
n/2 × ( a + l) = nth sum
n/2 × ( 1 + 121) = 671
n/2 × 122 = 671
61 n = 671
n = 11
a) so there are 11 terms
then,
so as 11th term is 121
let's find common diff
a + ( n-1) d = nth term
1 +( 11-1) d= 121
10d = 121 -1
10d = 120
common difference = 12
Please answer this correctly without making mistakes
Answers
Answer:
2/7
Step-by-step explanation:
Joseph bought a cheese and cut it into 7 equal pieces, so the denominator is 7.
Saved 5 pieces for cooking.
Gave 2 pieces to Omar.
Hope this helps :) ❤❤❤
Answer:
Step-by-step explanation:
if he gives to Omar 2 pieces of 7
2/7 = 28.57% for Omar rest of is for himself
The towers of a suspension bridge are 450 feet apart and 150 feet high from the roadway. Cables are at a height of 25 feet above the roadway, midway between the towers, but gradually get taller toward each end. Assume the x-axis is the roadway and the y-axis is the center of the bridge, write an equation for the parabola. What is the height of the cable at a point 50 feet from one of the towers? Round to the nearest whole number.
Answers
Answer:
y = 1/405 x² + 25
101 feet
Step-by-step explanation:
The vertex of the parabola is (0, 25).
The equation of the parabola is:
y − 25 = a (x − 0)²
y = ax² + 25
Two points on the parabola are (-225, 150) and (225, 150).
Plugging in one of those points:
150 = a (225)² + 25
125 = 50625 a
a = 1/405
The equation is therefore:
y = 1/405 x² + 25
50 feet from a tower is 175 feet from the center.
y = 1/405 (175)² + 25
y ≈ 101
At noon a passenger train leaves the Dupont Railway station and travels due east for 2 hours. At 12:45 pm the same day a second passenger train leaves the same railway station and travels due west for 1 hour and 15 minutes at a speed 10 kilometers per hour slower than the first passenger train. At 2pm the two trains were 215 kilometers apart. How fast had each train been traveling
Answers
Answer:
The speed of the first train is 70 km/hr
The speed of the second train is 60 km/hr
Step-by-step explanation:
For the first train:
Travel time = 2 hours
The speed = ?
we designate the speed as V
For the second train:
The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)
speed = 10 km/hr slower than that of the first train, we can then say
the speed = V - 10
The total distance traveled by both trains in the opposite direction of one another is 215 km
we can put this problem into an equation involving the distance covered by the trains.
we know that distance = speed x time
the distance traveled by the first train will be
==> 2 hrs x V = 2V
the distance traveled by the second train will be
==> 1.25 hrs x (V - 10) = 1.25(V - 10)
Equating the above distances to the total distance between the trains, we'll have
2V + 1.25(V - 10) = 215
2V + 1.25V - 12.5 = 215
3.25V = 215 + 12.5
3.25V = 227.5
V = 227.5/3.25 = 70 km/hr this is the speed of the first train
Recall that the speed of the second train is 10 km/hr slower, therefore
speed of the second train = 70 - 10 = 60 km/hr
The speed of the trains are 70km/hr and 60km/hr respectively.
The distance of the first train will be represented by: = 2 × D = 2D
The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).
Based on the information given in the question, the equation to solve the question will be:
2D + 1.25(D - 10) = 215
Collect like terms
2D + 1.25D - 12.5 = 215
3.25D = 215 + 12.5
3.25D = 227.5
D = 227.5/3.25
D = 70km/hour
The speed of the second train will be:
= 70 - 10 = 60km per hour.
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The sum of two positive integers is 37. When the smaller integer is subtracted from twice the larger, the result is 41. Find the two integers.
Answers
Answer:
26 and 11
Step-by-step explanation:
When your add them you get 37, and when you multiply 26 by two you get 52. 52-11 is 41.
What is (6b +4) when b is 2?
Answers
Answer:
16
Step-by-step explanation:
6*2 = 12
12 + 4 = 16
WHY CAN'T ANYONE HELP ME :( Solve the formula for the specified variable. tex]D=\frac{1}{4}fk for f.
Answers
Answer:
4d/k or [tex]\frac{4d}{k}[/tex]
Step-by-step explanation:
first multiply both sides by four
you will have 4d=fk
then divide by k
4d/k=f