#1 42% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut.

Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities

#2 Seventy-one percent of adults in a certain country believe that life on other planets is plausible. You randomly select five adults and ask them whether they believe that life on other planets is plausible. The random variable represents the number of adults who believe that life on other planets is plausible.

Find the mean, variance, and standard deviation of the binomial distribution for the random variable. Interpret the results.

#3 A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1537 and the standard deviation was 318. The test scores of four students selected at random are 1970, 1280, 2260, and 1440. Find the z-scores that correspond to each value and determine whether any of the values are unusual.

The z-score for 1970 is

The z-score for 1280 is

The z-score for 2260 is

The z-score for 1440 is

Which values, if any, are unusual?

#4 You work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. The manufacturer claims that the life spans of the tires are normally distributed, with a mean of 40,000 miles and a standard deviation of 4500 miles. You test 16 tires and get the following life spans.

47,796 38,994 26,166 38,135 32,858 42,661 43,038 36,969 25,742 31,099 38,252 37,645 31,709 38,099 38,388 43,512

Find the mean and standard deviation for the sample?

#5 Assume the random variable x is normally distributed with mean =88 and standard deviation

=4. Find the indicated probability.

P(x<86)=

#6 Assume the random variable x is normally distributed with mean =80 and standard deviation =4. Find the indicated probability.

P(67

#7 In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 21.1 and a standard deviation of 5.5.

(a) The probability of a student scoring less than 19

#8 Use the normal distribution of SAT critical reading scores for which the mean is 505 and the standard deviation is 108. Assume the variable x is normally distributed.

(a) What percent of the SAT verbal scores are less than 675?

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

#9 The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 6 minutes.

Find the probability that a randomly selected athlete uses a stairclimber for (a) less than 20 minutes, (b) between 24 and 33 minutes, and (c) more than 40 minutes.

#10 Use the normal distribution of Standardized Test scored for which the mean is 19.4 and standard deviation is 5.3.

(a) What percent of the scores are less than 19?

(b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21?