1. Richard has been given a 12-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. Assuming that Richard guesses on all 12 questions, find the probability that he will answer all questions correctly? Round your answer to the nearest hundredth.
A. 0.00
B. 0.50
C. 0.33
D. 0.25
E. 0.02
There are 5 radar stations and the probability of a single radar station detecting an enemy plane is 0.75. What is the probability that the number of stations that detect a plane is no more than 2? Round your answer to nearest hundreth.
A. 0.01
B. 0.75
C. 0.10
D. 0.09
E. 0.35
Richard has been given a 9-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. Assuming that Richard guesses on all 9 questions, find the probability that he will answer no more than 2 questions correctly? Round your answer to the nearest thousandth.
A. 0.738
B. 0.044
C. 0.500
D. 0.222
E. 0.302
Compute the expected age of a British nurse in 1851. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Round your answer to nearest hundredth.
Age range (yr)
2029
3039
4049
5059
6069
7079
80
Midpoint (x)
24.5
34.5
44.5
54.5
64.5
75.5
84.5
Percent of nurses
5.7
9.8
19.4
29.3
25.0
9.0
1.8
A. 54.50
B. 53.82
C. 53.79
D. 43.82
E. 59.50
Jim has a 5-year-old car in reasonably good condition. He wants to take out a $60,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:
= age
5
6
7
8
9
(accident)
0.01191
0.01292
0.01396
0.01503
0.01613
Jim is applying to a car insurance company for his car insurance policy. Using the probabilities that the car will have an accident in its 5th, 6th, 7th, 8th, or 9th year, and the $60,000 accident benefit, what is the expected loss to Car Insurance Company for the respective years? Round your answers to the nearest dollar.
A. $715, $775, $838, $892, $968
B. $715, $780, $838, $892, $968
C. $705, $780, $838, $902, $968
D. $715, $775, $838, $902, $968
E. $705, $775, $838, $892, $968
Give an example of a continuous random variable.
A. The number of traffic accidents in a city
B. The number of fish caught by a fishing boat
C. The number of coins contained in a slot machine
D. The number of tables sold at a furniture store
E. The number of gallons of water in a reservoir
The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $33. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 18 cookies. Lisa’s expected earnings can be found by multiplying the value of the dinner by the probability that she will win. How much did she effectively contribute to the hiking club?
A. $35.17
B. $31.97
C. $15.15
D. $17.17
E. $16.17
The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $36. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 719 cookies before the drawing. Lisa bought 35 cookies. Lisa