probability question statistics homework help

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1. The number of beverage cans produced each hour from a vending machine is normally distributed with a standard deviation of 8.6. For a random sample of 12 hours, the average number of beverage cans produced was 326.0. Assume a 99% confidence interval for the population mean number of beverage cans produced per hour.Calculate the margin of error of the 99% confidence interval.

2. The bias of an unbiased estimator is equal to 1. True or false

3. Are medical students more motivated than law students? A randomly selected group of each were administered a survey of attitudes toward Life, which measures motivation for upward mobility. The scores are summarized below. State the null and alternative hypotheses to determine if the mean score of medical students differs from the mean score of law students.

Medical Students

Law Students

Sample Size

250

100

Mean Score

83.5

80.2

4. A town has 500 real estate agents. The mean value of the properties sold in a year by these agents is $950,000, and the standard deviation is $200,000. A random sample of 100 agents is selected, and the value of the properties they sold in a year is recorded.

a. What is the standard error of the sample mean?

b. What is the probability that the sample mean exceeds $961,000?

c. What is the probability that the sample mean exceeds $943,000?

d. What is the probability that the sample mean is between $935 comma 000 and $959,000?

5. In a recent survey of 600 adults, 16.4% indicated that they had fallen asleep in front of the television in the past month. Which of the following intervals represents a 98% confidence interval for the population proportion?

6. A clinic offers a weight-loss program. The table below gives the amounts of weight loss, in pounds, for a random sample of 20 of its clients at the conclusion of the program. Assume that the data are normally distributed. 24 19 6 11 12 18 20 17 22 14 14 9 15 8 17 22 13 15 13 24

  • Find a 95% confidence interval for the population mean. The 95% confidence interval is from a lower limit of—-to an upper limit of ——(Round to two decimal places as needed.)
  • Without doing the calculations, explain whether a 90% confidence interval for the population mean would be wider than, narrower than, or the same as that found in part (a)

7. If the standard error of the sampling distribution of the sample proportion is 0.0229 for samples of size 400, then the population proportion must be either:

8. Why is the central limit theorem important in statistics?

9. Suppose that 70% of all tax returns lead to a refund. A random sample of 100 tax returns is taken.

a. What is the mean of the distribution of the sample proportion of returns leading to refunds? (Round to two decimal places as needed.)

b. What is the variance of the sample proportion? (Round to six decimal places as needed.)

c. What is the standard error of the sample proportion? (Round to four decimal places as needed.)

d. What is the probability that the sample proportion exceeds 0.80? (Round to four decimal places as needed.)

10. A school bus driver records the time (in minutes) it takes to commute to school for six days. Those results are: 25, 22, 17, 20, 15, and 10. Assuming the population is normally distributed, develop a 90% confidence interval for the population mean. Find the upper confidence limit of the 90% confidence

11. A 95% confidence interval estimate for a population mean μ is determined to be 65.48 to 76.52. Which of the following is true if a 90% confidence interval for μ is constructed?

12. A dependent random sample from two normally distributed populations gives the results shown below. Complete parts a and b below.

n=11            d=21.2            sd=3.7

  • Find the 90% confidence interval for the difference between the means of the two populations. The 90% confident interval is from a lower limit of____ to an upper limit of ___.(Round to one decimal place as needed.)
  • Find the margin of error for a 90% confidence interval for the difference between the means of the two populations.The margin of error ME= ___.(Round to one decimal place as needed.)

13. Based on the central limit theorem, the mean of all possible sample means is equal to the population:

14. In a random sample of 500 California residents, 350 indicated that they were home owners. In another random sample of 700 Florida residents, 455 indicated that they were home owners. What is the 99% confidence interval for the difference between the proportions?

15. The mean of the sampling distribution of the difference between sample proportions, ˆp1 – ˆp2, is equal to the difference between the corresponding population proportions, P1- P2. True of False

16. While constructing a confidence interval for the mean difference in paired data, as the sample size increases, the width of the interval also increases. True of False

17. Which of the following is an example of a continuous random variable?

A. The weight of a bag of potatoes.

B. The total points scored in a basketball game.

C. The number of repairs at a computer shop over the course of the week.

D. The number of cars in a parking lot.

18. A random sample of 100 voters is taken to estimate the proportion of a state’s electorate in favor of increasing the gasoline tax to provide additional revenue for highway repairs. Suppose that it is decided that a sample of 100 voters is too small to provide a sufficiently reliable estimate of the population proportion. It is required instead that the probability that the sample proportion differs from the population proportion (whatever its value) by more than 0.05 should not exceed 0.075. How large a sample is needed to guarantee that this requirement is met? The sample size n needs to be at least ____. (Round up to the nearest whole number.)

19. Suppose that 15% of all invoices are for amounts greater than $1,000. A random sample of 60 invoices is taken. What is the probability that between 13% and 23% of these 60 invoices are for more than $1,000?

20. If the random variable Z follows a standard normal distribution, then sigma StartFraction 2 Over z EndFraction= 1. True or false

21. A random variable X is normally distributed with a mean of 144 and a variance of 144, and a random variable Y is normally distributed with a mean of 160 and a variance of 256. The random variables have a correlation coefficient equal to -0.5. Find the mean and variance of the random variable below. W=6X-8Y.

µw=___ (Type an integer or a decimal.)

Ϭ²w=____ (Type an integer or a decimal.)

22. Anticipated consumer demand in a restaurant for free range steaks next month can be modeled by a normal random variable with mean 1100pounds and standard deviation 90pounds.

a. What is the probability that demand will exceed 900 pounds? (Round to four decimal places as needed.)

b. What is the probability that demand will be between 1,000 and 1,200pounds? (Round to four decimal places as needed.)

c. The probability is 0.15 that demand will be more than how many pounds? (Round to one decimal place as needed.)

23. Suppose that a random sample of 122 graduate-admissions personnel was asked what role scores on standardized tests play in consideration of a candidate for graduate school. Of these sample members, 73 answered “very important.” Find a 95% confidence interval for the population proportion of graduate admissions personnel with this view. The 95% confidence interval is from __ to__. (Round to four decimal places as needed.)

24. Which of the following statements is true regarding the width of a confidence interval for a population proportion?

A. It is narrower when the sample proportion is 0.20 than when the sample proportion is 0.50.

B. It is wider for a sample of size 80 than for a sample of size 40.

C. It is wider for 95% confidence than for 99% confidence.

D. It is narrower for 95% confidence than for 90% confidence.

25. As the size of the sample increases, what happens to the shape of the sampling distribution of sample means?

26. Given an arrival process with λ = 4.0, what is the probability that an arrival occurs after t = 4 time units? (Round to four decimal places as needed.)

27. If the standard error of the sampling distribution of the sample proportion is 0.02049 for samples of size 500, then the population proportion must be either:

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