(A)What Is the Percent of Pregnancies That Last More Than 300 Days?

AP StatName

Semester Review

1.The length of pregnancies from conception to natural birth among a certain female population is a normally distributed random variable with mean 270 and standard deviation 10 days.

(a)What is the percent of pregnancies that last more than 300 days?

(b)How short must a pregnancy be in order to fall in the shortest 10% of all pregnancies?

2.The National Collegiate Athletic Association (NCAA) requires Division I athletes to score at least 820 on the combined mathematics and verbal parts of the SAT exam in order to compete in their first college year. (Higher scores are required for students with poor high school grades.) In 1999, the scores of the more than one million students taking the SATs were approximately normal with mean 1017 and standard deviation 209. What percent of all students had scores less than 820?

3. A certain psychologist counsels people who are getting divorced. A random sample of six of her patients provided the following data where

x = number of years of courtship before marriage, and

y = number of years of marriage before divorce.

x30.521.55

y 96141020

a. Use your calculator to determine the least-squares regression line (LSRL).

b. What is the correlation between x and y? Interpret this number.

c. Show how the residual for the first data point in the table.

4. Cell phones, a recent innovation, have become increasingly popular with all segments of our society. According to the Strategis Group, the number of cellular and personal communications systems subscribers in the United States have increased dramatically since 1990, as shown in the following table.

No.of Subscribers

Year (millions)

1990 5.3

1991 7.6

1992 11.0

1993 16.0

1994 24.1

1995 33.8

1996 43.4

a.Apply a test to show that the cellular systems are increasing exponentially.

b. You want to construct a model to predict cell phone growth in the near future. Perform linear regression on the transformed data. Write your LSRL equation. What is the correlation for the transformed data?

c. Now transform your linear equation back to obtain a model for the original data.

Write the equation for this model.

d. Strategis Group predicts 70.8 million subscribers in 1998, and 99.2 million in the year 2000. How many cellular subscribers does your model predict for these years?

5. Suppose there are 500 students in your school. Using Line 125 of table B toselect the first 5 students in a simple random sample (SRS) of 20 students.

Read the article about the connection between vitamin E and heart bypass surgery.

6.Describe the experimental units/subjects in the experiment. How many were there?

7.Identify the explanatory variable(s).

8.How many treatments were there? ____ List them.

9.How many subjects were in each treatment group?

10.What was the response variable?

11. A die is loaded so that the number 6 comes up three times as often as any other number. What is the probability of rolling a 1 or a 6?

12. In a particular game, a fair die is tossed. If the number of spots showing is either four or five, you win $1. If the number of spots showing is six, you win $4. And if the number of spots showing is one, two, or three, you win nothing. You are going to play the game twice.

a. The probability that you win $4 both times is?

b. The probability that you win at least $1 both times is?

13. An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1.

a. The conditional probability of A given B

b. Are A and B independent?

14.Many fire stations handle emergency calls for medical assistance as well as those requesting fire fighting equipment. A particular station says that the probability that an incoming call is for medical assistance is 0.85. This can be expressed as P(call is for medical assistance) = 0.85.

(a)What is the probability that a call is not for medical assistance?

(b)Assuming that successive calls are independent of one another, calculate the probability that two successive calls will both be for medical assistance.

(c)Still assuming independence, calculate the probability that for two successive calls, the first is for medical assistance and the second is not for medical assistance.

(d)Still assuming independence, calculate the probability that exactly one of the next two calls will be for medical assistance.

15.Heart disease is the #1 killer today. Suppose that 8% of the patients in a small town are known to have heart disease. And suppose that a test is available that is positive in 96% of the patients with heart disease, but is also positive in 7% of patients who do not have heart disease. If a person is selected at random and given the test and it comes out positive, what is the probability that the person actually has heart disease?

16. A box contains ten $1 bills, five $2 bills, three $5 bills, one $10 bill, and one $100 bill. A person is charged $20 to select one bill.

a. Identify the random variable. X =

b. Construct a probability distribution for this data.

c. Find the expected value.

d. Is the game fair? Explain briefly.

16. Patients receiving artificial knees often experience pain after surgery. The pain is measured on a subjective scale with possible values of 1 to 5. Assume that X is a random variable representing the pain score for a randomly elected patient. The following table gives part of the probability distribution for X.

X 1 2 3 4 5

P(X).1.2.3.3

a.Find P(X = 5).

b.Find the probability that the pain score is less than 3.

c.Find the mean µ for this distribution.

d.Find the variance and standard deviation for this distribution.