Write up steps:

A) Assumptions

B) Sampling Distribution (show sketch)

C) Probability calculation

D) Interpretation of results

1. According to the article,"Song Dialects and Colonization in the House Finch" (Condor

(1975): 407- 422) reported the mean value of song duration for the population of house

finches is 1.5 min with a standard deviation of .9 min. Suppose an SRS of 25 finches is

selected. How likely is it that the average song duration of the sample will be greater than 1.7

min?

2. A soft drink bottler claims that, on average, cans contain 12 oz. of soda. Suppose the true

distribution of soda volumes is normally distributed with a mean of 12 oz. and a standard

deviation of .16 oz. Sixteen cans are randomly selected and their volumes are measured.

What is the probability the average volume will be between 11.96 and 12.08 oz.?

3. A hot dog manufacturer claims its most popular brand of weenie has an average fat content

of 18 g per hot dog. Suppose the standard deviation of the fat content of all hot dogs is 1 g.

An independent testing organization selects an SRS of 36 hot dogs and finds the average fat

content is 18.4 g. Does this result indicate the manufacturer's claim is incorrect?

4. The time a randomly selected individual waits for an elevator in an office building has a

uniform distribution with a mean of 0.5 min and standard deviation of 0.289 min. What are

the mean and standard deviation of the sampling distribution of means for SRS of size 50?

Does it matter that the underlying population distribution is not normal? What is the

probability a sample of 50 people will wait longer than 45 seconds for an elevator?

5. A manufacturing process is designed to produce bolts with a 0.5 in diameter. Once each

day, a random sample of 36 bolts is selected and the average diameter is calculated. If the

sample mean is less than 0.49 in or greater than 0.51 in, the process is shut down for

adjustment. The standard deviation for the production process is .02 in. What is the

probability the process will be shut down on any given day?

6. Suppose the mean value of interpupillary distance for all adult males is 65 mm and the

population 5 mm. If 25 adult males are selected, what is the probability the average distance

for all 25 will be between 64 and 67 mm?

7. Using the information from problem 6, answer the following questions: a) Approximately

95% of the time, the sample mean falls between______ and ______ b) Approximately .3% of

the time, the sample mean is farther than ________ from the true mean.