Problem # 1. The National Health Interview Survey reports that 41% of the telephone users no longer use landlines, and have switched completely to cell phone use. Suppose we take random sample of 10 telephone users. Use the table below to answer the question a.

X P = 0.41

0 0.0051

1 0.0355

2 0.1111

3 0.2058

4 0.2503

5 0.2087

6 0.1209

7 0.0480

8 0.0125

9 0.0019

10 0.01

a) Find the probability that the sample contains at least 5 users who have abandoned their landlines? Show all your steps

Hint P(X at least 5) = P( X= 5)+ P( X= 6)+ P( X= 7)+ P( X= 8)+ P( X= 9)+ P( X= 10)

b)Assume that the National Health Interview Survey reports that 44% of telephone users no longer use landlines, and have switched completely cell phone use. Suppose we take a random sample of 10 telephone users. Find the probability that the sample contains exactly 5 users who have abandoned their landlines? Show all your steps.

Problem # 2. The following frequency distribution table represents the time (in seconds) it takes the victim of a crime to call the police. Find the class width, class midpoints, class boundaries, the relative frequency and the cumulative frequency?

Time Frequency blank blank blank blank blank

0 -59 1

60-119 2

120-179 5

180-239 14

240-299 7

300-359 12

360-419 9

Construct a frequency histogram? Show all your steps.

Problem # 3. A recent study of 28 city residents showed that the mean of the time they had lived at their present address was 9.3 years. The standard deviation of the population was 2 years. Find the 90% confidence interval of the true mean? Assume that the variable is approximately normally distributed. Show all your steps.

Problem # 4. In a sample of 150 residents, each person was asked if he or she favored the concept of having a single countrywide police agency. The residence (city or outside the city) and the responses of the residents are summarized in the following table.

Residence Favor (F) Oppose (A)

In City (C ) 80 40

Outside of City (OC) 20 10

If one of these residents is selected at random,

a) what is the probability that the person will favor the concept given that the person selected is a city resident? Show all your steps.

b) what is the probability that the person will favor the concept given that the person selected is a resident from outside the city? Show all your steps.

c) what is the probability that the person will favor the concept or the person selected is a city resident? Show all your steps.

d) what is the probability that the person will favor the concept or the person selected is a resident from outside the city? Show all your steps.

Problem # 5. The number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is approximately normally distributed with the standard deviation = 10.

a) What is the probability that a randomly selected chocolate bar will have between 200 and 220 calories? Hint use the formula given on for z-score and then use the ztable. Show all your steps.

b) What is the probability that a randomly selected chocolate bar will have less than 190 calories? Hint use the formula given on for z-score and then use the z-table. Show all your steps.

Problem # 6. Dr. Mendoza developed a test to measure boredom tolerance. The test results for the group of 20,000 adults are shown in the following table. Determine if the table satisfies a probability distribution. If yes, find the mean, variance, and standard deviation? Show all your steps.

X P(X) X *P(X) (X- )^ 2 ( X - ) 2 *P(X)

0 0.07

1 0.13

2 0.18

3 0.30

4 0.22

5 0.10

Problem # 7. The president of a large university wishes to estimate the average age of the students presently enrolled. From past studies, the standard deviation of the population is known to be 2 years. A sample of 50 students is selected, and the mean is found to 23.2 years. Find the 95% confidence interval of the population mean? Show all your steps

Problem # 8. In a small summer course, Professor Blinky wants to compare the number of homeworks completed to final grades as shown in the table below.

X (Homeworks Completed) 6 8 4 2 6

Y (Final Grades) 82 93 78 40 70

blank x y xy x^2 y^2

6 82 492 36 6724

8 93 744 64 8649

4 78 312 16 6084

2 40 80 4 1600

6 70 420 36 4900

26 363 2048 156 27957

(a) Find the correlation coefficient (r)? Show all your steps.

(b) Find the regression equation? Show all your steps.

(c) Plot this regression line equation on a graph paper?

Problem #9. The average number of pounds of meat that a person consumes a year is 218.4 pounds. Assume that the standard deviation is 25 pounds and the distribution is approximately normal. If a sample of 40 individuals is selected, find the probability that the mean of the sample will be less than 224 pounds per year. Hint use the formula for z . Show all your steps.

Problem #10. A company makes Citi bikes. 90% (i.e., 0.90) pass final inspection. Suppose that 5 bikes are randomly selected. Hint use binomial distribution formula

a) What is the probability that exactly 4 of these 5 sports bikes pass final inspection?

b) What is the probability that less than 3 of these 5 sports bikes pass final inspection?