The reading speed of second grade students is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm. (a) What is the probability a randomly selected student will read more than 95 words per minute?
(b) What is the probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute?
(c) What is the probability that a random sample of 24 second grade students results in a mean reading rate of more than 95 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 20 second grade students was 92.8 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?