The reading speed of second grade students in a large city is approximatelynormal, with a mean of 92 letters 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 97 letters perminute?

If 100 different students were chosen from thispopulation, we would expect ____ to read more than 97 letters per minute.

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 97 letters perminute?

If 100 independent samples of n=12 students were chosen from thispopulation, we would expect ___ sample(s) to have a sample mean reading rate of less than 97 letter per minute.

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 97 letters perminute?

If 100 independent samples of n=24 students were chosen from thispopulation, we would expect ___ sample(s) to have a sample mean reading rate of exactly 97 letters per minute.

d. What effect does increasing the sample size have on theprobability? 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 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 increases as n increases.

(e) A teacher instituted a new reading program at school. After 10 weeks in theprogram, it was found that the mean reading speed of a random sample of 18 second grade students was 94.3 wpm. What might you conclude based on thisresult? Select the correct choice below and fill in the answer boxes within your choice.

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

A.

A mean reading rate of 94.3 wpm is unusual since the probability of obtaining a result of 94.3 wpm or more is ___. This means that we would expect a mean reading rate of 94.3 or higher from a population whose mean reading rate is 92 in

nothing

of every 100 random samples of size n=18 students. The new program is abundantly more effective than the old program.

B.

A mean reading rate of 94.3 wpm is not unusual since the probability of obtaining a result of 94.3 wpm or more is ___. This means that we would expect a mean reading rate of 94.3 or higher from a population whose mean reading rate is 92 in

nothing

of every 100 random samples of size n=18 students. The new program is not abundantly more effective than the old program.

(f) There is a5% chance that the mean reading speed of a random sample of 23 second grade students will exceed whatvalue?

There is a5% chance that the mean reading speed of a random sample of 23 second grade students will exceed ___ wpm.