#7 (2 Points) Explain what is meant by this statement: "There is not just one normal distribution but a "family" of them."

#9 (5 points) The mean of a normal probability distribution is 500; the standard deviation is 10. For b, d, and e you can round to whole percentage values (no decimals required). No calculations required for this problem--just use the normal distribution to answer the questions. Tip: To arrive at your answers draw a normal curve and label it with the mean, and deviation points.

a) About 68% of the observations lie between what two values?

b) About what percentage of the observations lie between 510 and and 520?

c) About 95% of the observations lie between what two values?

d) About what percentage of the observations are below 500?

e) About what percentage of the observations are between 490 and 530?

#11 (6 points) The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college two years ago, and each is now earning $70,000 per year. Rachel works in the retail industry, where the mean salary for executives with less than five years' experience is $55,000 with a standard deviation of $8,000. Rob is an engineer. The mean salary for engineers with less than 5 years' experience is $80,000 with a standard deviation of $5,000. Compute the z values for both Rob and Rachel.

#15 (9 points) The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of $29.81 per hour and a standard deviation of $9.31 per hour. What is the probability that the hourly pay of a randomly selected flight attendant:

a) Is between the mean and $35 per hour?

b) Is more than $35 per hour?

c) is less than $20 per hour?

#21 (3 points) WNAE, an all news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in for between 10 and 12 minutes?

#26 (4 points) The SAT reasoning test is perhaps the most widely used standardized test for college admissions in the United States. Scores for the SAT reasoning test are normally distributed with a mean of 1,500 and a standard deviation of 300. Clinton College would like to offer honors scholarships to students who score in the top 10% on this test. What is the minimum score qualifying students for the scholarship. (Answer not in the back of the book. Method to find was covered in class and there is a video tutorial).

#51 (5 points) A recent graduate from a business college is hired by a marketing firm. Her first year's estimated income is $35,000. She did research on starting salaries for similar positions and found that starting salaries are normally distributed with a mean of $33,500 and a standard deviation of $2,000. One day, she called a fellow alumnus who had a very similar position with a different firm and reported that his annual income was more than $50,000. Based on the research, what is the probability that person would have a starting salary of $50,000 or more? What can you conclude? (a brief statement of your conclusions).