The distribution of the amount of money undergraduate students spends on books for a term is slightly right-skewed, with a mean of $400 and a standard deviation of S80. If a simple random sample of 100 undergraduate students is selected, what is the probability that these students spend, on average, more than $425 on books?
Answers
The probability that on average these students spend more than $425 on books is given as follows:
0.0009 = 0.09%.
How to obtain the probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]
The desired probability is one subtracted by the p-value of Z when X = 425, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{425 - 400}{8}[/tex]
Z = 3.125.
Z = 3.125 has a p-value of 0.9991.
1 - 0.9991 = 0.0009 = 0.09%.
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Related Questions
Show that 100 divided by 20 is 5, using at least five daily life examples.
Answers
The 5 life examples are:
You have 100 pieces of candy and you want to divide them equally among 20 people. Each person would get 100/20 = 5 pieces of candy.A pizza is cut into 100 slices, and you want to divide it evenly among 20 people. Each person would get 100/20 = 5 slices of pizza.You have 100 dollars and you want to spend them on 20 items at the same price. Each item would cost 100/20 = 5 dollars.You want to divide a 100-minute task into 20 equal parts. Each part would take 100/20 = 5 minutes.You are scheduling 100 appointments in a day and you want to divide them into 20-hour blocks. Each block would have 100/20 = 5 appointments.What are the Life examples about?In all these life examples that are listed above, the number 100 is divided by 20 giving 5 as the result. which is said to be:
100/20
= 5.
Therefore, reason behind this is that the number 20, in these life examples, is a representative of a whole value and the number 5 represents the number of parts it is being divided into, so when you multiply 20 by 5, you get 100, which represents the total of these five parts. So, 100 is related to 20 in this context as the multiple of 20 and 5.
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1.
How many degrees does the hour hand of
a clock turn in 5 minutes?
(A)1/2
(B)3 1/2
(C) 5°
(D)2 1/2
Answers
Answer:
The answer is D (2 1/2)
Hope u helped
can someone please help me it’s for earth science
Answers
Answer:
20 mm
95 mm
75 mm
3 inches
0.15 in/yr
Step-by-step explanation:
From the graph :
Sea height variation January 2000 = 20 mm
Sea height variation January 2020 = 95 mm
Difference in height variation :
Height 2020 - Height 2000
95mm - 20mm = 75mm
Expressing in inches
1mm = 0.04 inches
75mm = (75 * 0.04)in
= 3 inches
Rate of increase :
Difference in sea level height / difference in time
3 / (2020 - 2000)
3 / 20
= 0.15
Find the slope of the line.
Answers
Answer:
line is negative, so -3/4
Step-by-step explanation:
probability...
a spinner has an equal chance of landing on either red, blue, green, or yellow. You spin five times. What is the probability that spinner lands on yellow exactly two times
Answers
Answer:
[tex]\frac{27}{1024}[/tex]
Step-by-step explanation:
So the chance of getting yellow is 0.25
Getting it once is 0.25
Getting it twice is 0.25 • 0.25
Not getting it is 0.75
So we have 0.25 • 0.25 • 0.75 • 0.75 • 0.75 = [tex]\frac{27}{1024}[/tex]
A small box measures 8 in. by 10 in. by 3/4 in. high. Find the volume of the box.
Answers
Answer:
Step-by-step explanation:
60
8x10x3/4
In a village, the cases of a particular infectious
disease have been exponentially decreasing at
a rate of 95% per year since the people started
receiving the vaccine. If there were 200 cases
in the village to start with, predict the number
of cases after 2 years.
First, complete the equation:
Remaining Amount = 200(1-0.95)²
Answers
The number remaining in the village is 30.
How many people remain?We have to note that the case in which the population of the community is being reduced because of the fact that the community is being ravaged by disease is a case of a decrease in the population and is a problem of exponential decrease.
Then we would have that;
N =Noe^-rt
N = Number at time t
No = Initial number
r = spread rate
t = time taken
Then;
N = 200e^-0.95 * 2
N = 30
Thus, they would have only 30 people left.
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how much does each nested cart add to the length of the row?
Answers
Each nested cart add to the length of the row is 1.5 feet long.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, the store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.
Each row has a starting cart that is 4 feet long, and the nested carts are next to it.
It is measured that a row of 13 nested carts has a length of 23.5 feet.
Therefore, the original length of 13 nested carts is (23.5 - 4) = 19.5 feet.
So, each nested cart add to the length of the row 19.5/13 =1.5 feet
Again, a row of 18 nested carts to be 31 feet long.
Therefore, the actual added length of 18 nested carts is (31 - 4) = 27 feet.
So, each nested cart add to the length of the row 27/18 =1.5 feet
Therefore, each nested cart add to the length of the row is 1.5 feet long.
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"Your question is incomplete, probably the complete question/missing part is:"
A store is designing the space for rows of nested shopping carts. Each row has a starting cart that is 4 feet long, followed by the nested carts (so 0 nested carts means there's just the starting cart). The store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.
How much does each nested cart add to the length of the row?
If m∠A = 29°, m∠B = 84°, and c = 14, what are the measures of the remaining sides and angle?
Answers
Answer:
m∠C = 67°, a = 7.37, b = 15.13
Step-by-step explanation:
There are 180° in a triangle. We know two angles in the triangle, so we can calculate the third angle.
Since this is not a right triangle, we will use the Law of Sines.
SinA/a = SinB/b = SinC/c
see image.
Samuel has $65, before he got his paycheck. Let y represent the amount of Samuels paycheck. Which expression can be used to find the amount of money that Samuel has after he received his paycheck?
Answers
Answer:
y + 65
Step-by-step explanation:
Given :
Amount Samuel had prior to receiving paycheck = $65
Amount of Samuel's paycheck = y
Amount Samuel has after receiving paycheck :
Sum of initial amount and paycheck value
y + 65
can you help with this please its urgent.
Answers
1. 60% of 330 would fill 6 of the boxes.
2. 45% of 600 would fill 4 and half of the boxes.
3. 42% of 450 is 189.
4. 79% of 800 is 632.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
1. The strip has 10 boxes and totals to 330.
Now, 60% of 330 would fill 6 out of those 10 boxes.
2. The strip has 10 boxes and totals to 600.
So, 45% of it would fill 4 and a half of the boxes.
3. 42% of 450 can be numerically expressed as,
(42/100)×450.
= 189.
Similarly, 4. 79% of 800 is,
(79/100)×800.
= 632.
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The gray figure below is the image of the black figure after a dilation. Which represents the dilation?
A (x,y) -> (2x, 2y)
B (x,y) -> (3x, 3y)
C (x,y) -> (0.5x, 0.5y)
D (x,y) -> (x+4, y+5)
Answers
The answer is A (x,y) -> (2x, 2y) it is representing the dilation.
What is dilation?Dilation is a medical procedure that involves widening a part of the body, such as the cervix or esophagus, by stretching and enlarging it. This can be done for a variety of reasons, including to allow for the passage of a baby during childbirth or to facilitate the insertion of a medical instrument or device. Dilation is usually done using dilators, which are cylindrical tools with a tapered end that can be inserted into the body and then gradually increased in size.
Dilation is a geometric transformation that enlarges or reduces the size of a shape by a factor. In this case, the shape is enlarged, with the resulting shape being twice the size of the original black figure. This is represented by the equation A (x,y) -> (2x, 2y), where the x and y coordinates of each point in the figure are multiplied by two.
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what is the value of x in the equation shown below x^3+1=9
Answers
Answer:
x = 2
Step-by-step explanation:
x^3 + 1 = 9
x^3 = 8
[tex]\sqrt[3]{x^3}[/tex] = [tex]\sqrt[3]{8}[/tex]
x = 2
Please help
Part A
Which is the vertex form of the function f(x) = 3x2 – 30x + 71?
O
A. 3(x - 5)2 - 4
B. 2(x – 6)2 - 1
C. 3(x – 4)2 + 23
D. 5(x – 4)2 – 9
Part B.
What is the vertex of the function?
vertex = (
Answers
Answer:
Option A:
y = 3*(x - 5)^2 - 4
Step-by-step explanation:
For a quadratic equation:
y = a*x^2 + b*x + c
with the vertex (h, k), we can rewrite the function as:
such that:
h = -b/2*a
y = a*(x - h)^2 + k
Here we have the function:
y = 3*x^2 - 30*x + 71
the x-value of the vertex will be:
h = -(-30)/(2*3) = 30/6 = 5
And k is given by:
k = y(5) = 3*(5)^2 - 30*5 + 71 = -4
Then the vertex is:
(5, - 4)
And we can rewrite the equation in the vertex form as:
y = 3*(x - 5)^2 + (-4)
y = 3*(x - 5)^2 - 4
Then the correct option is A.
Can someone help plz
Answers
Answer:
I never did this sort of stuff so correct me if I am wrong but I think it's 25
Step-by-step explanation:
In the School of ICT, one person in 80, on average, has blood of type O. If 200 student blood donors are taken at random, find an approximation to the probability that they include at least five persons having blood of type O. How many student donors must be taken at random in order that the probability of including at least one student donor of type O shall be 0.9 or more
Answers
The probability that they include at least five persons having blood of type O is given as follows:
0.1075 = 10.75%.
The number of donors needed so that the probability of including at least one student donor of type O shall be 0.9 or more is of 184 donors.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of the parameters for this problem are given as follows:
n = 200, p = 1/80 = 0.0125.
The probability of less than five is given as follows:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Using a binomial distribution calculator, these probabilities are given as follows:
P(X = 0) = 0.0808. P(X = 1) = 0.2046.P(X = 2) = 0.2576.P(X = 3) = 0.2153.P(X = 4) = 0.1342.Hence the probability of less than five successes is given as follows:
P(X < 5) = 0.0808 + 0.2046 + 0.2576 + 0.2153 + 0.1342 = 0.8925.
Hence the probability of at least five is given as follows:
P(X >= 5) = 1 - P(X < 5) = 1 - 0.8925 = 0.1075.
The probability of at least one is given as follows:
P(X >= 1) = 1 - P(X = 0)
P(X >= 1) = 1 - (1 - 0.0125)^n.
This probability is of 0.9 when:
1 - (1 - 0.0125)^n = 0.9
(0.9875)^n = 0.1
log((0.9875)^n) = log(0.1)
nlog(0.9875) = log(0.1)
n = log(0.1)/log(0.9875)
n = 183.1.
Rounding up, at least 184 donors must be surveyed.
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22 -- Here is a solid made from a square-based pyramid and a cube.
Each edge of the solid has length 6 cm.
On the centimetre grid, draw the plan of this solid.
How do I draw the plan
Answers
Answer:
Step-by-step explanation:
The solid's plan, consisting of a pyramid with a square base and a cube whose edges are each 6 cm long, will be represented in the attached graph.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
To draw the plan of a solid made from a square-based pyramid and a cube, with each edge having a length of 6 cm, you can start by drawing the top view of the cube. Since the edges of the cube have a length of 6 cm, the top view of the cube will be a square with sides of 6 cm.
Next, you can draw the top view of the square-based pyramid.
A square-based pyramid is a pyramid with a square base, so the top view of the pyramid will be a square with sides of 6 cm, just like the top view of the cube. However, the top view of the pyramid will also have four triangular faces extending from the corners of the square, each with a height of 6 cm.
To complete the plan of the solid, you can simply place the top view of the pyramid on top of the top view of the cube, aligning the edges of the squares.
The resulting drawing will be the plan of the solid made from a square-based pyramid and a cube, with each edge having a length of 6 cm.
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What is the domain of the function f(x)=√x?
Answers
Answer:
Interval: [0,∞), solution: x≥0.
Answer:
Domain: (0,+∞)
Step-by-step explanation:
negative numbers cannot have a square root taken unless your working with imaginary numbers.
Only question b
b) Write down the output y in terms of x
Input = x > +7 > x5 > Output = y
Answers
Therefore ,As a result, y = 5x + 35 is the equation that gives the answer to the given algebra issue.
Algebra: What Is It?Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols. The PEMDAS rule stands for the following operations: parenthesis, exponent, multiplication, division, addition, and subtraction. This rule is applied to solve the equation properly and accurately.
Here,
In this case, the equation for y in terms of x will be as follows:
y = 5(x + 7)
If you make the equation simpler, you get
y = 5(x + 7)
y = 5x + 35
y will have the linear equation y = 5x + 35 in terms of x.
Therefore , As a result, y = 5x + 35 is the equation that gives the answer to the given algebraic issue.
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i need help on this for math class dont mind how i answered a
Answers
Step-by-step explanation:
I think its c cus its more relatable .
Answer:
c would be the answer.
when you answer the equation x - 15= 60
you would add 15 to 60 to get 75. That is the only answer that would make sense.
YZ ≅ VW, WX ≅ UV, and XY ≅ UZ. Complete the proof that △UVZ ≅ △XWY.
Answers
8.) △UVZ ≅ △XWY
Reason: Side-Side-Side postulate
I need an answer fast
Answers
Alright I got it.
So first what I did was I made an equation that match did the word problem.
The equation was 15x=250+10x
When I solved it the answer was 50.
so they would need to sell 50 Tshirts (x=50)
A sample of 14 cans of Brand I diet soda gave the mean number of calories of 23 per can with a standard deviation of 3 calories. Another sample of 16 cans of Brand II diet soda gave the mean number of calories of 25 per can with a standard deviation of 4 calories. At the 1% significance level, can you conclude that the mean number of calories per can are different for these two brands of diet soda? Assume that the calories per can of diet soda are normally distributed for each of the two brands and that the standard deviations for the two population are equal.
Answers
Answer:
ठथठलछंशू फथजलट एक ओज पनि हो र स्वार्थी यसलाई मैले कसरी भुल्न सक्थेँ र त्यहाँको बडेमाको बिल्डिङ भित्र म. म जिन्दगी एक यात्रा तय गर्न गर्ने हो र त्यहाँको बडेमाको बिल्डिङ बनाउनलाई मुख्य समाचार पृष्ठ सभकेँ रिफ्रेश कए देखू। म भने त्यो भने हेर्न
write 363 in the base-four system
Answers
Answer:
363 = 11223₄
Step-by-step explanation:
You want 363 written in base 4.
Base conversionWe can convert to base 4 by looking at the remainders from repeated division by 4:
363 ÷ 4 = 90 r 3
90 ÷ 4 = 22 r 2
22 ÷ 4 = 5 r 2
5 ÷ 4 = 1 r 1
1 ÷ 4 = 0 r 1
Writing the remainders in reverse order gives the base-4 number:
363 = 11223₄
The length of a pencil is 128 mm correct to the nearest
millimetre.
Complete the error interval for the length of the pencil.
Give one value in each answer box.
mm < length
mm
Answers
Find the measure angles
No links for answers
Answers
Answer:
Angle L = 44
Angle M = 93
Angle O = 88
Angle P = 74
Step-by-step explanation:
First find your x, all angles will equal 360 when put together
360=61+x+(2x+5)+(x+30)+(2x)
360 = 61 + 5 +30 + x + 2x + x + 2x
360 - 96 = 6x
264 = 6x
264 / 6 = x
44 = x
Now place 44 in place of all x
Angle L:
x = 44
Angle M
(2x+5) = 2*44 + 5 = 93
Angle O
2x = 2*44 = 88
Angle P
(x+30) = 44 + 30 = 74
Parallel, intersecting, and perpendicular
Answers
The conditions of the line to be intersecting, parallel, and coincident are explained below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The types of lines are as follows:
If the slope of the lines is different, then the lines are intersecting lines.If the slope of the lines is the same but the y-intercept of the lines is different, then the lines are parallel lines.If the slope and y-intercept of the lines are the same, then the lines are coincident lines.More about the linear equation link is given below.
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Mr. Poppen joins a fitness club which has a cost represented by the function y = 10x + 70. Mrs. Zagorski joins a fitness club which has a cost represented by the function given by the ordered pairs: (0, 50), (1, 60), (2, 70), (3, 80). Who pays more initially, just to join the club?
Answers
Using the given function and the ordered pairs, we observed that Mr. Poppen pays more initially, to join the club
Calculating the initial costFrom the question, we are to determine who pays more initially to join the club between Mr. Poppen and Mrs. Zagorski
From the given information,
"Mr. Poppen joins a fitness club which has a cost represented by the function y = 10x + 70"
The initial amount paid by Mr. Poppen is the value of y when x is 0
y = 10x + 70
y = 10(0) + 70
y = 0 + 70
y = 70
From the given ordered pairs
(0, 50)
(1, 60)
(2, 70)
(3, 80)
We can conclude that the initial amount paid by Mrs. Zagorski is 50
Hence, Mr. Poppen pays more initially
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What's the pattern of 1, 2, 4, 5, 7, 8, 10
Answers
Answer:
U add 1 then add 2 for each number
Answer:
+1 then +2
Step-by-step explanation:
We are given a sequence of 1, 2, 4, 5, 7, 8, 10 and are asked to find the pattern.
To solve, we need to see how much is being added into every single number.
1, 2
+1
2, 4
+2
4, 5
+1
5, 7
+2
We see that there is a repetition of +1 and then +2.
Therefore the pattern is +1 then +2
A study was conducted to see if students from public high schools were more likely to attend public colleges compared to students from private high schools. Of a random sample of 100 students from public high schools, 60 were planning to attend a public college. Of a random sample of 100 students from private high schools, 50 of them planned to attend a public college. The 90% confidence interval for the difference between the proportion of students planning to attend public college between students at public versus private high schools is (-0.0152, 0.2152). Select the correct interpretation of this confidence interval.
a. Reject the null hypothesis
b. Fail to reject the alternative hypothesis
c. Accept the null hypothesis
d. Fail to reject the null hypothesis
Answers
Answer:
B
Step-by-step explanation:
We are 90% confident the proportion of students planning to attend public colleges who attended public high schools is between 0.0152 lower than to 0.2152 higher than the proportion of students planning to attend public colleges who attended private high schools.