The reading speed of second grade students in a large city is approximately normal, with a mean of

89

words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).

Question content area bottom

Part 1

(a) What is the probability a randomly selected student in the city will read more than

94

words per minute?

The probability is

. 3085.3085.

(Round to four decimal places as needed.)

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

3131

to read more than

94

words per minute.

Your answer is correct.

B.

If 100 different students were chosen from this population, we would expect

enter your response here

to read less than

94

words per minute.

C.

If 100 different students were chosen from this population, we would expect

enter your response here

to read exactly

94

words per minute.

Part 3

(b) What is the probability that a random sample of

12

second grade students from the city results in a mean reading rate of more than

94

words per minute?

The probability is

. 0418.0418.

(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 independent samples of

n=12

students were chosen from this population, we would expect

44

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

94

words per minute.

Your answer is correct.

B.

If 100 independent samples of

n=12

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

94

words per minute.

C.

If 100 independent samples of

n=12

students were chosen from this population, we would expect

enter your response here

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

94

words per minute.

Part 5

(c) What is the probability that a random sample of

24

second grade students from the city results in a mean reading rate of more than

94

words per minute?

The probability is

. 0071.0071.

(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 independent samples of

n=24

students were chosen from this population, we would expect

enter your response here

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

94

words per minute.

B.

If 100 independent samples of

n=24

students were chosen from this population, we would expect

11

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

94

words per minute.

Your answer is correct.

C.

If 100 independent samples of

n=24

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

94

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

increases as n increases.

B.

Increasing the sample size increases the probability because

x

increases as n increases.

C.

Increasing the sample size increases the probability because

x

decreases as n increases.

D.

Increasing the sample size decreases the probability because

x

decreases as n increases.

Your answer is correct.

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

91.3

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

91.3

wpm is unusual since the probability of obtaining a result of

91.3

wpm or more is

enter your response here.

This means that we would expect a mean reading rate of

91.3

or higher from a population whose mean reading rate is

89

in

enter your response here

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

91.3

wpm is not unusual since the probability of obtaining a result of

91.3

wpm or more is

. 1515.1515.

This means that we would expect a mean reading rate of

91.3

or higher from a population whose mean reading rate is

89

in

1515

of every 100 random samples of size

n=20

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

Your answer is correct.

Part 9

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

25

second grade students will exceed what value?

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

25

second grade students will exceed

enter your response here

wpm. (Round to two decimal places as needed.)