Question

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

92 words per minute​ (wpm) and a standard deviation of 10 wpm.

​(a) What is the probability a randomly selected student in the city will read more than 97 words per​ minute?

Interpret this probability.

(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 words per​ minute?

Interpret this probability.

(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 words per​ minute?

Interpret this probability.

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

(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 21 second grade students was 94.3 wpm. What might you conclude based on this​ result?

(f) There is a​ 5% chance that the mean reading speed of a random sample of 25 second grade students will exceed what​ value?

Answer 1

Let "X" be a student in the city

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

A mean rate of 94.3 wpm is not unusual since the probability of obtaining a result of 90.6 wpm or more is . The new program is not abundantly more effective than the old program.

From Z-table, Lookup for Z-value corresponding to area 0.05 to the right of the normal curve.