Question

An institute reported that

65%

of its members indicate that lack of ethical culture within financial firms has contributed most to the lack of trust in the financial industry. Suppose that you select a sample of 100 institute members. Complete parts (a) through (d) below.

Keep at least three decimal places for the standard error in order to get an answer close to the solution in the system.

a. What is the probability that the sample percentage indicating that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry will be between

57%

and

69%?

0.752

(Type an integer or decimal rounded to four decimal places as needed.)

b. The probability is

70%

that the sample percentage will be contained within what symmetrical limits of the population percentage?  

Hints:  (1) shade the middle 70% of the curve.  (2) change decimals to percentages after finished with calculations.

The probability is

70%

that the sample percentage will be contained above

nothing%

and below

nothing%.

(Type integers or decimals rounded to one decimal place as needed.)

c. The probability is

97%

that the sample percentage will be contained within what symmetrical limits of the population percentage?

The probability is

97%

that the sample percentage will be contained above

nothing%

and below

nothing%.

(Type integers or decimals rounded to one decimal place as needed.)

d. Suppose you selected a sample of 400 institute members. How does this change your answers in (a) through

(c)?

A.

An increase in sample size decreases the standard error, causing the value of the answer to part (a) to decrease and the ranges in parts (b) and (c) to narrow.

B.

An increase in sample size decreases the standard error, causing the value of the answer to part (a) to increase and the ranges in parts (b) and (c) to narrow.

C.

An increase in sample size increases the standard error, causing the value of the answer to part (a) to increase and the ranges in parts (b) and (c) to widen.

D.

An increase in sample size increases the standard error, causing the value of the answer to part (a) to decrease and the ranges in parts (b) and (c) to widen.