2 Math Assignments

all work must be shown the first assignment is due thursday december 5th the 2nd is due thursday december 11th.

1. The Wood County sheriff classifies crimes by age (in years) of the criminal and whether the crime is violent or nonviolent. As shown below, a total of

150

crimes were reported by the sheriff last year.

(20 points)

Total

Under 20	20 to 40	40 or older		Total
Violent	27	41	14	82
Nonviolent	12	34	22	68
39	75	36	150

a. What is the probability of selecting a case to analyze and finding it involved a violent crime?

b. What is the probability of selecting a case to analyze and finding the crime was committed by someone less than 40 years old?

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

d. Given that the violent crime is selected for analysis, what is the probability the crime was committed by a person under 20 years old?

e. Two crimes are selected by Judge Tybo. What is the probability both are violent crimes?

2. A real estate agent has 10 properties that she shows. She feels that there is a 10% chance of selling any one property. The chance of selling any one property is independent of selling another property.

(12 points)

a. What probability distribution model would be appropriate for describing the number of properties sold?

b. Compute the expected number of properties to be sold.

c. Compute the standard deviation of the number of properties to be sold.

d. Compute the probability of selling exactly one property.

e. Compute the probability of selling exactly five properties.

f. Compute the probability of selling at least two properties.

3. A pediatric nurse is studying the number of babies born at a hospital with congenial defects. Data shows that on the average, one baby with a congenial defect is born per month.

(12 points)

a. What type of probability distribution is appropriate for this problem?

b. Find the expected number of babies born in one year with congenial defects.

c. Find the standard deviation of the number of babies born in one year with congenial defects.

d. Find the probability that no babies are born with congenial defects in one year.

e. Find the probability that at least one baby is born with a congenial defect in a year.

f. Find the probability that exactly 12 babies are born with congenial defect in a year.

4.
The turkeys found in a particular county have an average weight of 15.6 pounds with a standard deviation of 4.0 pounds. Forty-five turkeys are randomly selected for a county fair.

(12 points)

a. Find the probability that the average weight of the turkeys will be less than 14.5 pounds.

b. What is the probability that the average weight of the turkeys will be more than 17 pounds?

c. Find the probability that the average weight of the turkeys will be between 15 and 16 pounds.

5. A nutrition label for Oriental Spice states that one package of the sauce has 1,190 milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 200 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1,167.34 milligrams of sodium per package with a sample standard deviation of 252.94 mg

(12 points)

a. Find the p-value for the test of hypothesis that the sodium content is different than the nutrition label states.

b. Is the sufficient evidence to reject the null hypothesis at a significance level of 0.01?

6. The news program for KOPE, the local television station, claims to have 40% of the market. A random sample of 500 viewers conducted by an independent testing agency found 192 who claim to watch the KOPE news program on a regular basis.
(12 points)

b. Find the p-value for testing the hypothesis that the news program for KOPE does not have at least 40% of the market, as it claims.

c. Is there sufficient evidence to reject the hypothesis that KOPE does not have at least 40% of the market at the significance level of 0.05?

7. A survey is being planned to determine the mean amount of time corporation executives watch television. A pilot survey indicated that the mean time per week is 12 hours, with a standard deviation of 3 hours. It is desired to estimate the mean viewing time within one quarter hour. The 0.95 degree of confidence is to be used. How many executives should be surveyed?

(6points)

8. Suppose an atomic reactor has two independent cooling systems. The probability that cooling system A will fail is 0.010 and the probability that cooling system B will fail is 0.015.

(6 points)

a. Find the probability that both cooling systems fail simultaneously.

b. What assumption did you make in answering the above question?

9. Tom decides to pay $160 for a one-year life-insurance policy with coverage of $110,000. The probability of his living through the year is 0.999. What is his expected value for the insurance policy?

(4 points)

10. The Detroit Music Company has purchased the rights to 10 different songs and it plans to release a new CD with 5 of them.

(4 points)

a. How many different CDs are possible if the order of the songs is important?

b. How many different CDs are possible if the order of the songs is not important?

Answer for part a:________________

Answer for part b:________________