1. According to information from Consumer Reports, monthly charges for cell phone plans in the United States are normally distributed with mean = $62 and standard deviation s = $18.

(a) Draw a normal curve with parameters labeled and shade the region that represents the proportion of plans that charge less than $44.

(b) Suppose the area under the normal curve to the left of x = $44 is 0.1587. Provide two interpretations of this result.

2. 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)

3. Assume that the ight time for U.S. Airways ight 1267 from Philadelphia to Dallas follows the uniform probability distribution between 210 and 250 minutes. What is the probability that a randomly selected ight will take less than 224 minutes?

4. Find the values of z0.025

5. Find the z-scores that separate the middle 80% of the data from the area in the tails of the standard normal distribution.

6. Find the area under the standard normal curve

(a)to the left of z = 2.75, (b)to the right of z = 1.38

(c)to the right of z = 2.08 (d)between z = 1.05 and z = 2.52.

7. 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 426 and the standard deviation was 72. If the board wants to set the passing score so that only the best 80% of all applicants pass, what is the passing score? Assume that the scores are normally distributed.

8. A discrete random variable is given. Assume the probability will be approximated using a normal distribution. Describe the area under the normal curve that will be used to compute the probability of getting at most 80 successes

(a) Right of X = 80.5

(b) Right of X = 79.5

(c) Left of X = 80.5

(d) Left of X = 79.5

9. If the probability of a newborn kitten being female is 0.5, nd the probability that in 200 births, 120 or less will be female. Use the normal distribution to approximate the binomial distribution.

10. According to Gallup poll, 46% of Americans 18 years old or older stated that they had read at least six books (ction and nonction) within the past year. You conduct a random sample of 250 Americans 18 years old or older.

(a) Verify that the conditions for using the normal distribution to approximate the binomial distribution are met.

(b) Approximate the probability that exactly 125 read at least six books within the past year.

(c) Approximate the probability that fewer than 120 read at least six books within the past year.

(d) Approximate the probability that between 100 and 120, inclusive, read at least six books with in the past year.

11. My commute time to work during the week follows the normal probability distribution with a mean time of 25 minutes and a standard deviation of 4 minutes. What is the probability that the commute time for a randomly selected day will be between 22 and 30 minutes?

12. Assume the random variable X is normally distributed with mean = 50 and standard deviation s = 7. Find the 77th percentile.

13. A simple random sample of size n = 36 is obtained from a population with = 64 and standard deviation s = 18.

(a) Describe the sampling distribution of x ( x bar)

(b) What is P( x < 62.6)?

(c) What is P( x >_68.7)?

(d) What is P(59. < x < 65.9)?

14. Determine x and std x (standard deviation xbar) from the given parameters of the population and the sample size. = 84 std = 12, n = 64.

15. Suppose there is a normally distributed population with a mean of 250 and a standard deviation of 50. If x is the average of a sample of 36, nd the following probabilities.

(a) P( x <_240)

(b) P( x >_255)

(c) P(246<_ x <_260)

16. The average score for a water safety instructor (WSI) exam is 75 with a standard deviation of 12. Fifty scores for the WSI exam are randomly selected.

(a)Find the probability that the average of the fty scores is at least 80.

(b)Find the probability that the average of the fty scores is between 72 and 78.

17. A simple random sample of size n = 36 is obtained from a population with = 64 and (standard deviation) std = 18.

(a) Describe the sampling distribution of x.

(b) What is P( x < 62)?

(c) What is P(62 < x < 70)?

18. The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 3000 miles. What is the probability a particular tire of this brand will last longer than 65,000miles?

19. Suppose that the true proportion of registered voters who favor the Republican presidential candidate is 0.45. Find the mean and standard deviation of the sample proportion for a sample size of 65.

20. Suppose that the true proportion of Americans who save at least 10% of their income is 0.15. if p ( P hat) is the sample proportion of Americans surveyed who save at least 10% of their income from the sample of 68,nd the following probabilities.

(a) P( p > 0.25)

(b) P(0.18 < p < 0.25)