Which of the following describes the shape of the normal probability distribution?|Statistics
1. Which of the following that explains the shape of the normal probability distribution?
Positively skewed
Symmetrical
Always decreasing
Negatively skewed
2.
2. Apply the normalcdf feature on the calculator to find the specified area under the standard normal distribution curve. Round your answers to four decimal places (to the nearest ten-thousandth).
To the left of z = 1.10
3. check the probability below for the normal distribution with mean μ = 12.5 and standard deviation σ = 1.6. Give your answer as a percent rounded to the nearest hundredth (two decimal places).
P(13.8 < X < 14.6)
4. The average life of a brand of automobile tires is 30,000 miles, with a standard deviation of 2,000 miles. If a tire is selected and tested, find the probability that it will have a lifetime between 25,000 and 32,000 miles. Assume the variable is normally distributed. Give your answer as a percent rounded to two decimal places (to the nearest hundredth).
5. The average time it takes college freshmen to complete the Mason Basic Reasoning Test is 24.6 minutes. The standard deviation is 5.8 minutes.
Find the probability that the average completion time for a sample of 26 students will be more than 22 minutes. Give your answer as a percent rounded to two decimal places (to the nearest ten-hundredth).
6.
A random sample of n = 47 customers at a fast-food restaurant had a mean bill of xÌ… = $12.17. If the population standard deviation is σ = $1.92, find the 94% confidence interval (including units) of the mean bill for all customers. Assume the variable is normally distributed and state the distribution used to find the interval.
Distribution used:
Confidence interval:
7. The average age of a sample of n = 73 mayors was xÌ… = 46.9 years with a standard deviation of s = 3.1 years. Assuming the ages are normally distributed, find the 95% confidence interval (including units) of the mean age of all mayors. State the distribution used.
Distribution used:
Confidence interval:
8. In a certain convenient care center, a random sample of n = 31 weeks was selected. It was found that an average of xÌ… = 399 patients were treated per week with a standard deviation of s = 22.7. Assume the variable is normally distributed and find the 97% confidence interval (including units) of the population mean. State the distribution used.
Distribution used:
Confidence interval:
9. The recorded high temperatures (in degrees Fahrenheit) in June for a sample of 17 US cities are listed below. Assuming the temperatures are normally distributed, find the 92% confidence interval (including units) of the population mean. Give the distribution used and the mean and standard deviation of the sample rounded to the nearest hundredth (two decimal places). Give all digits provided by the calculator for the confidence interval.
95 73 84 80 88 84 76 102 67
98 103 89 104 98 86 91 92
Distribution used:
xÌ… ≈
s ≈
Confidence interval:
10. The GPAs for a sample of n = 6 freshmen at a certain college are listed below. Assuming the GPAs are normally distributed and that σ = 0.43, find the 98% confidence interval of the true mean of the freshman class (no units are needed). Give the distribution used and the mean of the sample rounded to the nearest hundredth (two decimal places). Give all digits provided by the calculator for the confidence interval.
1.93 2.85 2.58 3.12 2.07 2.19
Distribution used:
xÌ… ≈
Confidence interval:
11. A consumer advocate group claims that among smokers the average number of cigarettes smoked per day is higher than 20.
Select the correct comparison symbol that would go in the box below to complete the claim made in the statement.
Claim: μ ☠20
Question 1 options:
<
<
>
=
>
≠
12. Discuss the null hypothesis H0 and the alternative hypothesis H1 for the case study below.
In 1990, the average age at which women in the United States married for the first time was 23. A sociologist believes that the average age has increased and conducts a statistical test to check this claim.
Question 2 options:
H0: μ > 23
H1: μ < 23
H0: μ = 23
H1: μ ≠ 23
H0: μ > 23
H1: μ < 23
H0: μ < 23
H1: μ > 23
13. Complete steps 2 through 5 of the hypotheses test for the case study below. The hypotheses for step 1 are provided. Give the value of p rounded to the nearest ten-thousandth (to four decimal places). You can type H0 as Ho. A consumer advocacy group asserts that on average Americans pay more than $123 per month on television subscription services. A sample of n = 60 Americans paid an average of xÌ… = $127.14 for their cable or satellite service. If the standard deviation for the population is σ = $18.24, test the group’s claim at α = 0.10.
1. H0: μ < 123
H1: μ > 123 (claim)
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.3%2C%20HypTestSteps.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
14. Complete steps 2 through 5 of the hypotheses test for the case study below. The hypotheses for step 1 are provided. Give the value of p rounded to the nearest ten-thousandth (to four decimal places). You can type H0 as Ho. Mark Zuckerberg claims that the average number of friends on Facebook is a least 130 per user. The average number of Facebook friends for a sample of n = 38 users is xÌ… = 142. If the standard deviation for all Facebook users is σ = 38.2, test the claim at α = 0.10.
1. H0: μ > 130 (claim)
H1: μ < 130
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.3%2C%20HypTestSteps.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
15. The data below gives the number of pages, x, and the cost, y, for a sample of six textbooks. Note that the data given in this problem is not necessarily the same as in the other problems. Which of the following graphs shows the scatter plot and regression line for the data?
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20data%20set%203.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
Question 1 options:
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20scatter%20plot%203.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20scatter%20plot%205.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20scatter%20plot%201.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20scatter%20plot%204.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20scatter%20plot%202.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
16. The data below gives the number of pages, x, and the cost, y, for a sample of six textbooks. Note that the data given in this problem is not necessarily the same as in the other problems. Find the equation of the regression line, y = a + bx, and correlation coefficient r for the data. Round all values to the nearest thousandth (to three decimal places).
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20data%20set%203.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
17. The data below gives the number of pages, x, and the cost, y, for a sample of six textbooks. Note that the data given in this problem is not necessarily the same as in the other problems.
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20data%20set%201.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
Complete steps 2 through 4 of the hypotheses test for the correlation coefficient. The hypotheses for step 1 are provided. Give the value of p rounded to the nearest ten-thousandth (to four decimal places).
1. H0: ρ = 0 (not linear)
H1: ρ ≠ 0 (linear)
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20linreg%20steps.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
18. The data below gives prices (in dollars per pound) of six selected vegetables in Alaska, x, and the prices of the same vegetables in Georgia, y.
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20data%20set%2010.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
Complete steps 2 through 4 of the hypotheses test for the correlation coefficient. The hypotheses for step 1 are provided. Give the value of p rounded to the nearest ten-thousandth (to four decimal places).
1. H0: ρ = 0 (not linear)
H1: ρ ≠ 0 (linear)
https://albanystate.view.usg.edu/content/enforced/1573724-CO.220.MATH2411.52498.20191/Homework/HW%205.4%2C%20linreg%20steps.JPG?_&d2lSessionVal=DrRKEZqeRqxsxXnuOUoRz1GSr
19. The high temperature (in degrees Fahrenheit), x, and the ice cream sales (in dollars) for a local store, y, are related by the regression line equation y = -365.469 + 8.637x.
Find the amount of sales predicted by the model if the high temperature is x = 84°F. Give your answer as a monetary amount rounded to the nearest cent.
