# Probability , hypothesis and confidence interval

I would like help with the following exercises for future reference and a better overall understanding. Thanks!

1. The Los Angeles sheriff classifies crimes by age (in years) of the criminal and whether the crime is violent or nonviolent. As shown below, the sheriff reported a total of 150 crimes last year.

Age (in years)

Type of Crime Under 20 20 ~ 40 Over 40 Total

Violent 27 41 14

Non Violent 12 34 22

Total

a. What is the probability of selecting a case that involved non-violent crime?

b. What is the probability of selecting a case that was committed by a person over 20 yrs age?

c. What is the probability of selecting a case that involved a violent crime or an offender less than 20 yrs old?

d. Judge Tybo selects two crimes for review. What is the probability that both are violent crimes?

2. Ontario Apartments has a large number of units available to rent each month. A concern of management is the number of vacant apartments each month. A recent study revealed the percent of the time that a given number of apartments are vacant. Compute the mean and standard deviation of the number of vacant apartments.

Number of

Vacant Units Probability

0 .1

1 .4

2 .2

3 .2

4 .1

MEAN:

Std. Dev:

3. The mean starting salary for college graduates in the Spring of 2006 was $50,000. Assume that the distribution of starting salaries follows the normal distribution with a standard deviation of $3500. What percent of the graduates have starting salaries:

a. Between $40000 and $60000?

b. More than $40000?

4. Suppose you record how long it takes you to get to work (or school) over many months and discover that the times are approximately bell-shaped with a mean of 15 minutes and a standard deviation of 2 minutes. How much time should you allow to get there to make sure you are on time 90% of the time or more? Please show your work.

5. The average qualifying speed for a championship NASCAR race is 145.65 mph and the standard deviation is 9.45 mph. Only drivers who obtain z-scores greater than 1.2 will qualify for the race. If the speeds are normally distributed, what minimum speed must be clocked to compete for the trophy?

a. 146.9 mph b. 155.2 mph

c. 157.0 mph d. 174.8 mph

Use the following information for questions 6 ~ 7.

Consider the following frequency distribution that shows the distribution of shoe sizes in a women's clothing store:

Shoe Size Pairs in stock

5

6

7

8

9 15

25

40

30

20

The department manager makes a random selection of a pair of shoes to show a customer.

6. The probability that the selected shoe is a size 7 or larger is

a. 0.38 b. 0.40

c. 0.69 d. 1.0

7. The probability that the selected shoe is size 6 or less is

a. 0.12 b. 0.19

c. 0.31 d. 1.0

Use the following information for questions 8 ~ 10.

An airline company completed an on-board passenger survey of 400 customers in an attempt to measure the number of bags checked by those traveling on business or for pleasure. Results are shown in the table below:

Passenger 0 Checked 1 Checked 2 Checked 3 or more Total

Business

Pleasure 50

20 60

80 30

90 10

60 150

250

Total 70 140 120 70 400

8. What is the probability that a customer either traveled on business or checked exactly 1 bag?

a. 0.150 b. 0.575

c. 0.875 d. 0.950

9. What is the probability that a customer was either traveling for pleasure or checked no bags?

a. 0.750 b. 0.625

c. 0.175 d. 0.800

10. What is the probability that a customer checked fewer than 2 bags?

a. 0.175. b. 0.525.

c. 0.825 d. 0.955

Use the following information for questions 11 ~ 12.

Approximately 25% of the population belongs to a health maintenance organization (HMO). Assume that for a randomly selected group of 20 adults, the number belonging to an HMO has a binomial distribution.

11. The probability of finding exactly 5 in the 20 who belong to an HMO is:

a. 0.2023 b. 0.1567

c. 0.1750 d. 0.2345

12 The probability of finding at most 7 in the 20 who belong to an HMO is:

a. 0.1455 b. 0.5143

c. 0.6578 d. 0.8982

13. According to police records, from 1987 to 1995, the city of Davis, California experienced the following burglary rate (offenses per 1,000 residents for a given year):

Year 1987 1988 1989 1990 1991 1992 1993 1994 1995

Rate 15.8 17.2 16.5 15.5 17.1 18.6 21.4 29.0 19.3

Using the t distribution, construct a 95% confidence interval for the mean annual burglary rate in Davis, California.

Use the following information to answer questions 14 and 15:

The batteries used in a digital watch have a operating life that is normally distributed. A sample of 16 batteries reveals a mean of 3.45 years and a standard deviation of 0.3 years.

14. The width of a 95% confidence interval is

a. 0.16 years.

b. 0.20 years.

c. 0.26 years.

d. 0.32 years.

15. The upper bound of a 90% confidence interval is

a. 3.55 years.

b. 3.58 years.

c. 3.61 years.

d. 3.65 years.

#### Solution Summary

This solution gives the step by step method for computing Probability , hypothesis and confidence interval for a set of problems.