The reading speed of second grade students in a large city is approximately normal, with a mean of 88 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).

Part 1

(a) What is the probability a randomly selected student in the city will read more than 92 words per minute?

Part 2

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

A.

If 100 different students were chosen from this population, we would expect to read less than 92 words per minute.

B.

If 100 different students were chosen from this population, we would expect to read exactly 92 words per minute.

C.

If 100 different students were chosen from this population, we would expect to read more than 92 words per minute.

Part 3

(b) What is the probability that a random sample of 13 second grade students from the city results in a mean reading rate of more than 92 words per minute?

The probability is

(Round to four decimal places as needed.)

Part 4

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

A.

If 100 different samples of n=13 students were chosen from this population, we would expect

sample(s) to have a sample mean reading rate of more than

92 words per minute.

B.

If 100 different samples of n=13 students were chosen from this population, we would expect

enter your response here sample(s) to have a sample mean reading rate of less than 92 words per minute.

C.

If 100 different samples of n=13 students were chosen from this population, we would expect

enter your response here sample(s) to have a sample mean reading rate of exactly

92 words per minute.

Part 5

(c) What is the probability that a random sample of 26 second grade students from the city results in a mean reading rate of more than 92 words per minute?

The probability is

enter your response here.

(Round to four decimal places as needed.)

Part 6

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

A.

If 100 different samples of n=26 students were chosen from this population, we would expect

sample(s) to have a sample mean reading rate of more than

92 words per minute.

B.

If 100 different samples of n=26 students were chosen from this population, we would expect

sample(s) to have a sample mean reading rate of exactly

92 words per minute.

C.

If 100 different samples of n=26 students were chosen from this population, we would expect

sample(s) to have a sample mean reading rate of less than

92 words per minute.

Part 7

(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.

A.

Increasing the sample size decreases the probability because x decreases as n increases.

B.

Increasing the sample size increases the probability because x decreases as n increases.

C.

Increasing the sample size increases the probability because x increases as n increases.

D.

Increasing the sample size decreases the probability because x increases as n increases.

Part 8

(e) A teacher instituted a new reading program at school. After 10 weeks in the program, it was found that the mean reading speed of a random sample of 20 second grade students was

90.6 wpm. What might you conclude based on this result? Select the correct choice below and fill in the answer boxes within your choice.

(Type integers or decimals rounded to four decimal places as needed.)

A.

A mean reading rate of 90.6 wpm is unusual since the probability of obtaining a result of

90.6 wpm or more is .

This means that we would expect a mean reading rate of 90.6 or higher from a population whose mean reading rate is 88 in of every 100 random samples of size

n=20 students. The new program is abundantly more effective than the old program.

B.

A mean reading rate of 90.6 wpm is not unusual since the probability of obtaining a result of

90.6 wpm or more is enter your response here.

This means that we would expect a mean reading rate of 90.6 or higher from a population whose mean reading rate is 88 in enter your response here of every 100 random samples of size

n=20 students. The new program is not abundantly more effective than the old program.

Part 9

(f) There is a 5% chance that the mean reading speed of a random sample of

21 second grade students will exceed what value?

There is a 5% chance that the mean reading speed of a random sample of

21 second grade students will exceed enter your response here wpm. (Round to two decimal places as needed.)