### Solution Found!

# Do you jog The Gallup Poll once asked a random sample of

**Chapter , Problem R7.4**

(choose chapter or problem)

**QUESTION:**

Do you jog? The Gallup Poll once asked a random sample of 1540 adults, Do you happen to jog? Suppose that in fact 15% of all adults jog.

(a) What is the mean of the sampling distribution of \(\hat{p}\)? Justify your answer.

(b) Find the standard deviation of the sampling distribution of \(\hat{p}\). Check that the 10% condition is met.

(c) Is the sampling distribution of \(\hat{p}\) approximately Normal? Justify your answer.

(d) Find the probability that between 13% and 17% of a random sample of 1540 adults are joggers. Show your work.

Use the sampling distribution of \(\hat{p}\) to evaluate a claim about a population proportion.

### Questions & Answers

**QUESTION:**

Do you jog? The Gallup Poll once asked a random sample of 1540 adults, Do you happen to jog? Suppose that in fact 15% of all adults jog.

(a) What is the mean of the sampling distribution of \(\hat{p}\)? Justify your answer.

(b) Find the standard deviation of the sampling distribution of \(\hat{p}\). Check that the 10% condition is met.

(c) Is the sampling distribution of \(\hat{p}\) approximately Normal? Justify your answer.

(d) Find the probability that between 13% and 17% of a random sample of 1540 adults are joggers. Show your work.

Use the sampling distribution of \(\hat{p}\) to evaluate a claim about a population proportion.

**ANSWER:**

Step 1 of 5

Given:

n = 1540

p = 15% = 0.15