Question

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).

(a) What is the probability a randomly selected student in the city will read more than 94 words per minute? The probability is (Round to four decimal places as needed.) 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 94 words per minute.

B. If 100 different students were chosen from this population, we would expect to read exactly 94 words per minute. C. If 100 different students were chosen from this population, we would expect to read more than 94 words per minute.

(b) What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more than 94 words per minute?

The probability is

(Round to four decimal places as needed.)

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

A. If 100 independent samples of n=10 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of less than 94 words per minute.

B. If 100 independent samples of n=10 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of more than 94 words per minute.

C. If 100 independent samples of n=1010 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of exactly 94 words per minute.

(c) What is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 94 words per minute?

The probability is

(Round to four decimal places as needed.)

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

A. If 100 independent samples of n=20 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of exactly 94 words per minute.

B. If 100 independent samples of n=20 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of less than 94 words per minute.

C. If 100 independent samples of n=20 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of more than 94 words per minute Your answer is correct.

(d) What effect does increasing the sample size have on the probability?

Provide an explanation for this result.

A. Increasing the sample size increases the probability because sigma Subscript x overbarσx increases as n increases.

B. Increasing the sample size decreases the probability because sigma Subscript x overbarσx decreases as n increases. Your answer is correct.

C. Increasing the sample size increases the probability because sigma Subscript x overbarσx decreases as n increases.

D. Increasing the sample size decreases the probability because sigma Subscript x overbarσx increases as n increases.

(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 19 second grade students was 91.9 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 91.9 wpm is unusual since the probability of obtaining a result of 91.9 wpm or more is This means that we would expect a mean reading rate of 91.9 or higher from a population whose mean reading rate is 89 in of every 100 random samples of size n=19 students. The new program is abundantly more effective than the old program.

B. A mean reading rate of 91.9 wpm is not unusual since the probability of obtaining a result of 91.9 wpm or more is . This means that we would expect a mean reading rate of 91.9 or higher from a population whose mean reading rate is 89 in of every 100 random samples of size n=19 students. The new program is not abundantly more effective than the old program.

Answer 1

Here we have

(a)

The z-score for x = 94 is

So the required probability is

Expected number of students = 100 * 0.3085= 30.85

Correct option is C

(b)

Sample size n=10

The z-score for is

So required probability is

Expected number of students = 100 * 0.0571 = 5.71

Correct option is B.

(c)

Sample size n=20

The z-score for is

So required probability is

Expected number of students = 100 * 0.0125 = 1.25

Correct option:

If 100 independent samples of n=28 students were chosen from this population, we would expect N=28 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of of more than 94 words per minute.

(d)

B. Increasing the sample size decreases the probability because sigma Subscript x overbarσx decreases as n increases.

(e)

Sample size n=19

The z-score for is

So required probability is

This probability is not unusual because this probability is greater than 0.05.

B. A mean reading rate of 91.9 wpm is not unusual since the probability of obtaining a result of 91.9 wpm or more is . This means that we would expect a mean reading rate of 91.9 or higher from a population whose mean reading rate is 89 in of every 100 random samples of size n=19 students. The new program is not abundantly more effective than the old program.