The reading speed of second grade students in a large city is approximately normal, with a mean of 90 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 more than 94 words per minute.

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

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

(b) What is the probability that a random sample of 14 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=14 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=14 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. If 100 independent samples of n=14 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) What is the probability that a random sample of 28 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=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 less than 94 words per minute.

B. 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.

C. 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 exactly 94 words per minute.

(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 oX decreases as n increases.

b. Increasing the sample size increases the probability because oX decreases as n increases.

c. Increasing the sample size decreasing the probability because oX increases as n increases.

d. Increasing the sample size increases the probability because oX 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 22 second grade students was 92.5 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 92.5 wpm is not unusual since the probability of obtaining a result of 92.5 wpm or more is . This means that we would expect a mean reading rate of 92.5 or higher from a population whose mean reading rate is 90 in of every 100 random samples of size n=22 students. The new program is not abundantly more effective than the old program.

b) A mean reading rate of 92.5 wpm is not unusual since the probability of obtaining a result of 92.5 wpm or more is . This means that we would expect a mean reading rate of 92.5 or higher from a population whose mean reading rate is 90 in of every 100 random samples of size n=22 students. The new program is abundantly more effective than the old program.

(f) There is a 5% chance that the mean reading speed of a random sample of 23 second grade students will exceed what value?

There is a 5% chance that the mean reading speed of a random sample of 23second grade students will exceed wpm.