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 from this population will read at more than 97 words per minute?

(b) What is the probability that a random sample of 12 secondgrade students from the city results in a mean reading rate of more than 97 words per minute?

(c) What is the probability that a random sample of 24 secondgrade students from the city results in a mean reading rate of more than 97 words per minute?

(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 94.6 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 20 second-grade students will exceed what value?