An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 2% of the true proportion with 99% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy?
Answer: n = 2401
Step-by-step explanation:
Given;
Confidence level = 2% - 99%
n = ? ( which is the sample size is unknown ).
Solution:
Where;
n = [z/E]^2*pq
Since no known value for ( p ) estimate is given, the "least biased" estimate is p = 1/2
Substituting the given data into the formula.
n = [1.96/0.02]^2(1/2)(1/2)
n = 2401
The minimum number of truck drivers the statistician needs to sample for an accurate result is 2401
Identify the percent, amount, and base in this problem What is 15% of 60?
Answer:
9
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
16. Use yesterday’s stock table for the company Icarus to answer the following questions.
52-week Price
High Low
Stock
Symbol
Dividend
Annual Yield Return (%)
P/E ratio
Volume Traded
High Low
Price Price
Closing Price
Net Change
28.38 15
Icarus
ICR
0.41
1.1
24
105300
24 23.5
24
. . . .
a. What was the high price for Icarus stock over the last 52 weeks?16a. _______________
b. If you owned 1000 shares of Icarus stock last year, what is the dollar amount of the b. _________________
dividend you received?
c. What is the annual yield return for dividends alone?c. _________________
d. How many shares of Icarus stock were traded yesterday?d. _________________
e. What was the low price for Icarus stock yesterday?e. _________________
f. What was the price of Icarus stock at the close of the stock exchange yesterday?f. _________________
g. Compute Icarus’s annual earnings per share using the formula below.g. _________________
2/3x + 5 = 3 plz helppppppp
Answer:
2 /3 +5 = 3
5.666667≠3
False
Step-by-step explanation:
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Lets do this step by step.
~~~~~~~~~~~~~~~~~~~~
Multiply both sides of the equation by [tex]\frac{3}{2}[/tex] .
[tex]\frac{3}{2} . \frac{2}{3} . x = \frac{3}{2} . 5[/tex]
Simplify both sides of the equation.
~~~~
Simplify [tex]\frac{3}{2} . \frac{2}{3} . x .[/tex]
[tex]x = \frac{3}{2} . 5[/tex]
Multiply [tex]\frac{3}{2} . 5[/tex]
[tex]x = \frac{15}{2}[/tex]
The result can be shown in multiple forms.
Exact Form: [tex]x = \frac{15}{2}[/tex]
Decimal Form: [tex]x = 7.5[/tex]
Mixed Number Form: [tex]x = 7\frac{1}{5}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
pls help me help me
Answer:
A
Step-by-step explanation:
For an inequality to have a shaded area above the graph, the variable has to be on the left side of a greater than sign, or a greater than or equal to sign.
A is the only option with one of these signs, so it is the correct answer.
What is the total of 49 1/4+3 3/8
Answer:
52 5/8
Step-by-step explanation:
To add fractions, you have to make sure both fractions have a common denominator.
As you can see, the fractions have different denominators, so to make both denominators 8, we have to multiply 1/4 by two, which gives us 2/8.
Then, we just add like normal!
49 2/8+ 3 3/8 = 52 5/8!
Hope this helped! :)
Professor Easy's final examination has 9 true-false questions followed by 3 multiple-choice questions. In each of the multiple-choice questions, you must select the correct answer from a list of five. How many answer sheets are possible? choices
Answer: 2⁹5³ = 64,000
Step-by-step explanation:
There are 9 questions with 2 options (true or false) = 2⁹
There are 3 multiple questions with 5 options = 5³
true/false questions AND multiple choice questions
2⁹ x 5³ = 2⁹5³
What are the expressions for length, width, and height?
Volume = length width height
V = _____ _____ _____
For odyyseyware
Answer:
[tex]\boxed{V=lwh}[/tex]
Step-by-step explanation:
The formula for volume of a cuboid is:
[tex]V=lwh[/tex]
[tex]volume = length \times width \times height[/tex]
Answer:
V = l w h
Step-by-step explanation:
Volume of a Cuboid = Length × Width × Height
Where l = length, w = width and h = height
What are the solutions of the quadratic equation (x – 8)2 - 13(x - 8) + 30 = 0? Use u substitution to solve.
Ox=-11 and x = -18
x= -2 and x = 5
x= 2 and x = -5
x= 11 and x = 18
Answer:
Its D
Step-by-step explanation:
x=11 and x=18
For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the new equation, find x if the point P(x, 4) lies on the new line. y=3x-1 y=1/4 x+2
Answer:
The answer is below
Step-by-step explanation:
a) y=3x-1
The standard equation of a line is given by:
y = mx + c
Where m is the slope of the line and c is the intercept on the y axis.
Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:
3 × d = -1
d = -1/3
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]
b) y=1/4 x+2
Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:
1/4 × f = -1
f = -4
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 34.9 lb.
a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 201 lb.
b. If 39 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 201 lb.
c. When redesigning the ejection seat which probability is more relevant?
Answer:
The answer is below
Step-by-step explanation:
Given that:
mean (μ) = 138 lb, standard deviation (σ) = 34.9 lb
z score is used in statistic to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{150-138}{34.9}=0.34[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma}=\frac{201-138}{34.9}=1.81[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(0.34 < z < 1.81) = P(z < 1.81) - P(z < 0.34) = 0.9649 - 0.6331 = 0.3318 = 33.18%
b) If 39 different pilots are randomly selected i.e. n = 39. For probability that his weight is between 150 lb and 201 lb, we need to calculate the z score for 150 lb and for 201 lb.
For 150 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{150-138}{34.9/\sqrt{39} }=2.15[/tex]
For 201 lb:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{201-138}{34.9/\sqrt{39} }=11.3[/tex]
From normal distribution table, probability that his weight is between 150 lb and 201 lb = P(150 < x < 201) = P(2.15 < z < 11.3) = P(z < 11.3) - P(z < 2.15) = 1 - 0.9842 = 0.0158 = 1.58%
c) The probability from part C is more important
helppp i will give stars,thanks and also bralienst
Answer:
21.30 dollarsis the answerStep-by-step explanation:
Total money/ number of people
63.90/3 = 21.30
If you divide by 3 then the 3 friends will get the equal amount of money.
Answer:
Step-by-step explanation:
The total amount of money is $63.90. Also, there are 3 friends.
In order to pay equally, divide $63.90 and 3 friends, so the answer would be dollars per friend
$63.90/3 friends = $21.3/friend
So the items you would drag would be:
2 $10 bills
1 $1 bill
3 $0.10 dimes
Evaluate the series
Answer:
the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
C) 59
Step-by-step explanation:
Recall that;
[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]
Therefore, we can evaluate the series;
[tex]\sum_{k=1}^{6}(25-k^2)[/tex]
by summing the values of the series within that interval.
the values of the series are evaluated by substituting the corresponding values of k into the equation.
[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]
So, the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
An entertainment company specifies that its employees must weigh between 40 kgs - 50 kgs. If X is the random variable denoting the weights of employees, X is a __________ random variable.
Answer: Continuous
If X is the random variable denoting the weights of employees, X is a continuous random variable.
Step-by-step explanation:
Given: An entertainment company specifies that its employees must weigh between 40 kgs - 50 kgs.
here weights of the employees vary.
Also, weight is measured not counted , that means weight is a continuous variable.
If X is the random variable denoting the weights of employees, X is a continuous random variable.
The weights of employees, X, is a: continuous random variable.
Facts about Random Continuous VariableA continuous variable is obtained simply through measuring.Examples of continuous variable are: weight of students, distance travelled.A continuous random variable are values given for an interval of numbers.Therefore, the weights of employees, X, is a: continuous random variable.
Learn more about continuous random variable on:
https://brainly.com/question/15238425
Find the indicated binomial probability. A multiple choice test has 30 questions, and each has four possible answers, of which one is correct. If a student guesses on every question, find the probability of getting exactly 12 correct.
Answer:
0.02906
Step-by-step explanation:
number of questions =30
getting exactly right : 12
30C12 the number of possibilities
probability to get it right (1/4)^12
probability of failure =1-1/4=(3/4)^18 ( 18 = 30 questions -12 right )
P(12)=30C12*(1/4)^12*(3/4)^18=0.02906
hope it helps
We draw a random sample of size 25 from a normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?
Answer:
11.2≤[tex]\mu[/tex]12.8Step-by-step explanation:
Confidence interval for the population mean is expressed by the formula;
CI = xbar ± Z(S/√n) where;
xbar is the sample mean = 12.5
Z is the z score at 99% confidence = 2.576
S is the standard deviation = √variance
S = √2.4 = 1.5492
n is the sample size = 25
Substituting the given values into the formula given above,
CI = 12.5 ± 2.576(1.5492/√25)
CI = 12.5 ± 2.576(0.30984)
CI = 12.5 ± 0.7981
CI = (12.5-0.7981, 12.5+0.7981)
CI = (11.2019, 12.7981)
Hence the 99% confidence interval for the population mean is 11.2≤[tex]\mu[/tex]12.8 (to 1 decimal place)
A 99% confidence interval for the population mean will be "11.2 [tex]\leq[/tex] 12.8".
StatisticsAccording to the question,
Sample mean, [tex]\bar x[/tex] = 12.5
Z score at 99%, Z = 2.576
Standard deviation, S = √Variance
= √2.4
= 1.5492
Sample size, n = 25
We know the formula,
Confidence interval, CI = [tex]\bar x \ \pm[/tex] Z ([tex]\frac{S}{\sqrt{n} }[/tex])
By substituting the given values, we get
= 12.5 [tex]\pm[/tex] 2.576 ([tex]\frac{1.5492}{\sqrt{25} }[/tex])
= 12.5 [tex]\pm[/tex] 2.576 (0.30984)
= 12.5 [tex]\pm[/tex] 0.7981
Now,
Cl = (12.5 - 0.7981, 12.5 + 0.7981)
= (11.2019, 12.7981) or,
= (11.2, 12.8)
Thus the above answer is appropriate.
Find out more information about mean here:
https://brainly.com/question/7597734
Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester.
University A University B
Sample Size 50 40
Average Purchase $280 $250
Standard Deviation $20 $23
At 95% confidence test to determine if, on the average, students at University A spend more on textbooks then the students at University B.
Answer:
Z > Zα
6.511 > 1.645
Step-by-step explanation:
University A University B
Sample Size 50 40
Average Purchase $280 $250
Standard Deviation $20 $23
We formulate
H0: x1` > x2` null hypothesis that the mean of the University A is greater than the mean of the University B
HA: x1`≤ x2` one tailed test
Test statistic
Z= x1`-x2`/ √s₁²/n₁ +s²₂/n₂
Z= 280-250/√400/50 + 529/40
Z= 30/√8 +13.225
Z= 30 /4.607
Z= 6.511
For one tailed test at α= 0.05 = 1.645
Z > Zα
6.511 > 1.645
Thus we reject null hypothesis.On the average, students at University A spend more on textbooks then the students at University B.
A tech company is curious about marketing their new drones for home security. Let the proportion of houses that have home security be p. If the tech company would like to know if the proportion of houses that have home security is different than 45%, what are the null and alternative hypotheses
Answer:
Step-by-step explanation:
The null hypothesis is described as the default hypothesis while the alternative hypothesis us always tested against this null ie the opposite of the null hypothesis.
In this case study, Let the proportion of houses that have home security be p
Thus, the null hypothesis is proportion of houses that have home security is 45% : p = 45%
The alternative hypothesis is proportion of houses that have home security is different than 45%: p =/ 45%
Find x.................
Answer:
90°
Step-by-step explanation:
Theres a right angke beside x
And Angles on a straight line = 180 so 180-90°= 90°
Answer:
90
Step-by-step explanation:
I looked it up on the internet
All sides of the building shown above meet at right angles. If three of the sides measure 2 meters, 7 meters, and 11 meters as shown, then what is the perimeter of the building in meters?
Answer:
Perimeter= 40 units
Step-by-step explanation:
Ok
We are asked to look for the perimeter.
We have some clue given.
All at right angle and some sides are given it's full length.
We have the bae to be 11 unit
The height to be 7 unit.
What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.
Let's go for the other side of the height.
Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.
So we have 7+7+11
But it's not complete yet.
We are given a dimension 2.
And the 2 is in two places so it's total 2*2= 4
The two is for a small base .
The base is actually an extra to the 11 of the other base.
So summing up
We have 2*11 + 2*7 + 2*2
Perimeter= 22+14+4
Perimeter= 40 units
Please show step by step working out of stationary points and points of inflection with the y coordinates (and sketch graph) for the equation y=x^4-36x^2
Answer:
See picture attached
Step-by-step explanation:
Given that r = ( 7, 3, 9) and v = ( 3, 7, -9), evaluate r + v
a. (-21,-21,81)
b. (10,10,0)
c. (21,21,-81)
d. (-10,-10,0)
Answer:
b. (10,10,0)
Step-by-step explanation:
r+v can be evaluated if the vectors/matrices have the same dimensions.
These do. They are both 1 by 3 vectors.
Just add first to first in each.
Just add second to second in each.
Just add third to third in each.
Example:
(5,-5,6)+(1,2,3)
=(5+1,-5+2,6+3)
=(6,-3,9)
Done!
In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).
r+v
=(7,3,9)+(3,7,-9)
=(7+3,3+7,9+-9)
=(10,10,0)
Done!
You visit a farm and notice that white chickens lay white eggs and colored chickens lay colored eggs, so you decide that only white chickens lay white eggs. What type of reasoning is this?
Answer:
This is called an Inductive reasoning.
Step-by-step explanation:
It is a logical process in which a number of premises all believed true combine to come up with specific conclusions. This is a generalisation based on observations.
Hope it helps.
A popular charity used 31% of its donations on expenses. An organizer for a rival charity wanted to quickly provide a donor with evidence that the popular charity has expenses that are higher than other similar charities. The organizer randomly selected 10 similar charities and examined their donations. The percentage of the expenses that those 10 charities spend on expenses is given below. Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether the mean is less than 31% and then draw a conclusion in the context of the problem. Use α=0.05. 26 12 35 19 25 31 18 35 11 26 Select the correct answer below: Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%. Reject the null hypothesis. There is insufficient evidence to conclude that the mean is less than 31%. Fail to reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%. Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is less than 31%.
Answer:
Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%.
Step-by-step explanation:
In this case we need to test whether the popular charity has expenses that are higher than other similar charities.
The hypothesis for the test can be defined as follows:
H₀: The popular charity has expenses that are higher than other similar charities, i.e. μ > 0.31.
Hₐ: The popular charity has expenses that are less than other similar charities, i.e. μ < 0.31.
As the population standard deviation is not known we will use a t-test for single mean.
Compute the sample mean and standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{10}\cdot[0.26+0.12+...+0.26]=0.238\\\\s= \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 0.0674 }{ 10 - 1} } =0.08654\approx 0.087[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{0.238-0.31}{0.087/\sqrt{10}}=-2.62[/tex]
Thus, the test statistic value is -2.62.
Compute the p-value of the test as follows:
[tex]p-value=P(t_{\alpha, (n-1)}<-2.62}[/tex]
[tex]=P(t_{0.05,9}<-2.62)\\=0.014[/tex]
*Use a t-table.
Thus, the p-value of the test is 0.014.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.014 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Thus, concluding that there is sufficient evidence to conclude that the mean is less than 31%.
The formula to convert Fahrenheit to Celsius is C=5/9(F-32). Convert 30c to Fahrenheit. Round to the nearest degree
Answer:
86 degrees farenheit
Step-by-step explanation:
First, we plug 30 in for C.
Next, solve for F
Multiplying both sides by 9/5 gives us 54=F-32
Add 32 to both sides 86=F
need help with this question
Answer:
[tex] - 2 {x}^{5} {y}^{7} [/tex]Last option is correct.
Step-by-step explanation:
[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]
Multiply the terms with the same base by adding their exponents
[tex] - 2 {x}^{3 + 2} {y}^{4 + 3} [/tex]
Add the numbers
[tex] - 2 {x}^{5} {y}^{7} [/tex]
Hope this helps..
Best regards!
[tex] - 2 {x}^{5} {y}^{7} [/tex]
Solution:
[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]
[tex] = 2 {x}^{(3 + 2)} {y}^{(4 + 3)} [/tex]
[tex] = - 2 {x}^{5} {y}^{7} [/tex]
[tex]{\boxed{\blue{\textsf{Some Important Laws of Indices}}}}[/tex]
[tex]{a}^{n}.{a}^{m}={a}^{(n + m)} [/tex]
[tex]{a}^{-1}=\dfrac{1}{a}[/tex]
[tex]\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}[/tex]
[tex]{({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}[/tex]
[tex] {a}^{\frac{1}{x}}=\sqrt[x]{a}[/tex]
[tex]a^0 = 1[/tex]
[tex][\text{Where all variables are real and greater than 0}][/tex]
The process of producing pain-reliever tablets yields tablets with varying amounts of the active ingredient. The manufacturer claims each tablet has at least 200 milligrams of the active ingredient. The consumer Watchdog Bureau assumes the manufacturer claim is correct, but occasionally tests samples of the tablets to ensure they contain enough of the ingredient. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The sample mean content of the active ingredient is 205.7 milligrams, while the sample standard deviation is 21 milligrams. What is the p-value for this test?
Answer:
The p-value is [tex]p-value = 0.013167[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu[/tex] = 200 milligrams
The sample size is [tex]n = 70[/tex]
The sample mean is [tex]\= x = 205.7[/tex]
The sample standard deviation is [tex]\sigma = 21 \ milligram[/tex]
Generally the Null hypothesis is mathematically represented as
[tex]H_o : \mu = 200[/tex]
The Alternative hypothesis is
[tex]H_a : \mu < 200[/tex]
The test statistics is mathematically represented as
[tex]t_s = \frac{\= x - \mu }{\frac{\sigma}{\sqrt{n} } }[/tex]
substituting values
[tex]t_s = \frac{ 205.7 - 200 }{\frac{21}{\sqrt{70} } }[/tex]
[tex]t_s = 2.270[/tex]
Now the p-value is mathematically represented as
[tex]p-value = P(Z \le t_s )[/tex]
substituting values
[tex]p-value = P(Z \le 2.270 )[/tex]
Using the Excel function[=NORMDIST(2.270)] to calculate the p-value we obtain that
[tex]p-value = 0.013167[/tex]
Answer:
A) 0.012
From CollegeBoard
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and standard deviation 7 ml. The fill
volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL?
1.0000
0.8810
0.8413
0.9987
Answer:
0.8413
Step-by-step explanation:
Find the z score.
z = (x − μ) / σ
z = (992 − 999) / 7
z = -1
Use a chart or calculator to find the probability.
P(Z > -1)
= 1 − P(Z < -1)
= 1 − 0.1587
= 0.8413
The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct
Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined
Probability can be defined as the ratio of favorable outcomes to the total number of events.
We use Z-statistic to find out the probability,
z = (x − μ) / σ
x = raw score = 992 mL
μ = population mean = 999 mL
σ = standard deviation
z = [992 − 999]/7
z = -1
P-value from Z-Table:
P(x<992) = 0.15866
P(x>992) = 1 - P(x<992) = 0.84134
Thus, the required probability that a bottle has a volume greater than 992 mL is 0.84134
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If ABC=DEC B=48 and E=C+4
x=?
Answer:44
Step-by-step explanation:the two triangles are congruent , so we deduce from that the angle B=angle E =48
So, x+4=48 , x=44 degree
A manufacturer claims that its rechargeable batteries are good for an average of more than 1.000 charges. A random sample of 100 batteries has a mean life of 1002 charges and a standard deviation of 14. Is there enough evidence to support this claim at a significance level of 0.01?
a. State the hypotheses.
b. State the test statistie information
c. State either the p-value or the critical information d. State your conclusion and explain your reasoning
It's 1000 charges and not 1.000 charges
Answer:
A)Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = 1.4286
C) p-value = 0.15628
D) We conclude that we will fail to reject the manufacturers claim that its rechargeable batteries are good for an average of more than 1000 charges
Step-by-step explanation:
We are given;
x = 1002 charges
s = 14
μ = 1000 charges
n = 100
degree of freedom = n - 1 = 100 - 1 = 99
A) The hypotheses are;
Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = (x - μ)/(s/√n)
(1002 - 1000)/(14/√100) = 1.4286
C) From the t-score calculator results attached, the p-value is approximately 0.15628
D) The P-value of 0.15628 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we conclude that the result is statistically nonsignificant.