preview

Normal Distribution and Random Sample

Decent Essays

Math 156–Sat: HW #4 Name:

1. What is the difference between [pic] and[pic]? Between s and[pic]? (10 points)

2. Explain the difference between [pic] and [pic] and between [pic] and[pic]? (10 points)

3. Suppose that a random sample of size 64 is to be selected from a population having [pic] and standard deviation 5.

(a) What are the mean and standard deviation of the [pic] sampling distribution? Can we say that the shape of the distribution is approximately normal? Why or why not? (10 points)

(b) What is the probability that [pic] will be within 0.5 of the population mean? (5 points)

(c) What is the probability that [pic] will differ from the population mean by more than …show more content…

medical residents who have credit card debt of more than $3000. (10 points)

(c) How many medical residents should be sampled in order to build a 99% confidence interval with an error of no more than 4%? (5 points)

10. The airborne times of United Airlines flight 448 from Albuquerque to Denver on 10 randomly selected days are shown below. You may assume that the flight times of all such flights are normally distributed. (10 points each)

57 54 55 51 56 48 52 51 59 59

(a) Find a 90% confidence interval for the mean airborne time for flight 448.

(b) Repeat part (a) if it is known that the standard deviation of such flights is 1.7 minutes.

11. The eating habits of 12 bats were examined in the article “Foraging Behavior of the Indian False Vampire Bat” (Biotropica [1991]). For these 12 bats, the mean time to consume a frog was [pic] minutes and the standard deviation was 7.7 minutes. Construct a 90% confidence interval for the mean time it takes this bat to consume a frog. What assumption(s) must be made here? (10 points)
Math 156–Sat: HW #4 - Solutions

1. [pic] is the mean of a sample whereas [pic] is the mean for the entire population

s is the standard deviation of a sample whereas [pic] is the standard deviation of the entire population

2. [pic] is the mean for the entire population whereas [pic] is the mean of the

Get Access