Q5.1

#1 In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.5 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below.

(a) Find the probability that a study participant has a height that is less than 66 inches.

(b) Find the probability that a study participant has a height that is between 66 and 72 inches.

c) Find the probability that a study participant has a height that is more than 72 inches.

(d) Identify any unusual events. Explain your reasoning.

#2 The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 20 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stairclimber for

(a) less than 16 minutes,

(b) between 20 and 28 minutes,

(c) more than 30 minutes.

#3 Use the normal distribution of SAT critical reading scores for which the mean is 510 and the standard deviation is 114. Assume the variable x is normally distributed.

(a) What percent of the SAT verbal scores are less than 550?

(b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525?