1. The heights of 10-year-old males are normally distributed with = 55.9 inches and s = 5.7inches.

(a) Draw a normal curve with the parameters labeled. Shade the region that represents the proportion of 10 year old males who are less than 46.5 inches tall.

(b) Suppose the area under the normal curve to the left of x = 46.5is0.0496. Provide two interpretation of this result.

2. Assume that the ight time for Delta Airlines ight DL870 from New York to Orlando follows the uniform probability distribution between 200 and 236 minutes. What is the probability that a randomly selected ight will take less than 224 minutes?

3. A continuous random variable X is uniformly distributed with 10<_ X <_50.

(a) Draw a graph of the uniform density function.

(b) What is P(20<_ X <_30)

(c) What is P(X < 15)

(d) What is P(X >_32)

4. Assumethattherandomvariable X isnormallydistributedwith = 50, and s = 7, compute

(a) P(X <_58)

(b) P(56 < X <_66)

(c) P(X > 35)

5. Find the area under the standard normal curve between z = 1.04 and z = 2.76.

6. A random variable follows the normal probability distribution with mean of 80 and standarddeviationof20. What is the probability that a randomly selected value from this population

(a) is less than 90?

(b) is more than 110?

(c) between 65 and 100?

7. Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 800 and standard deviation of 75. Find the probability that a randomly selected student will score

(a) less than 650

(b) between 700 and 850

(c) over 850

8. Find the z-score such that the area under the standard normal curve to the right is 0.0735.

9. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a random sample of 20 people have a mean IQ score greater than 110?

10. The U.S. Air Force requires that pilots have heights between 64 inches and 77 inches. Heights of women are normally distributed with mean of 63.7 inches and standard deviation of 2.9 inches. What percent of women meet that height requirements?

11. Find the z-scores that separate the middle 88% of the data from the area in the tails of the standard normal distribution.

12. Find the value of z0.04

13. Find the value of t0.005 if n = 36.

14. Find the t-value such that the area in the right tails 0.15 with 23 degrees of freedom.

15. Find the t-value such that the area in the left tail is 0.90 with 68 degrees of freedom.

16. Find ta 2 for a 95% condence and sample size n = 16.

17. In a poll conducted by the Gallup organization, 16% of adult, employed Americans were dissatised with the amount of their vacation time. You conduct a survey of 500 adult ,employed Americans.

(a) Use the normal approximation to the binomial to approximate the probability that exactly 100 are dissatised with their amount of vacation time.

(b) Use the normal approximation to the binomial to approximate the probability less than 60 are dissatised with their amount of vacation time.

(c) Use the normal approximation to the binomial to approximate the probability that atleast 155 are dissatised with their amount of vacation time.

18. Determine p and s p from the given parameters. Assume the size of the population is 25,000, n = 200, p = 0.75.

19. Determine x and sx from the given parameters of the population and the sample size. = 90 s = 40, n = 64.

20. The Social Media and Personal Responsibilities Survey found that 69% of parents are "friends" with their children on Facebook. A random sample of 140 parents was selected.

(a) Calculate the standard error of the proportion.

(b) What is the probability that between 96 and 105 parents from this sample are 'friends" with their children on Facebook?

21. According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population standard deviation is $0.50 and that the sample of 30 theaters was randomly selected.

(a) Calculate the standard error of the mean.

(b) What is the probability that the sample mean will be less than $7.75?

(c) What is the probability that the sample mean will be more than $8.20?

22. The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 550 and the standard deviation was 60. If the board wants to set the passing score so that only the best 70% of all applicants pass, what is the passing score? Assume that the scores are normally distributed.