Math 227 - Statistics » Spring 2023 » Midterm 2 Exam

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Question #1
In a genetics experiment on peas, one sample of offspring contained 244 green peas and 285 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   43.44
B.   46.12
C.   48.19
D.   49.72
Question #2
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant / A / B / C / D Order Accurate / 21 / 11 / 9 / 12 Order Not Accurate / 6 / 22 / 6 / 13 If one order is selected, find the probability of getting an order from Restaurant A or an order that is not accurate. Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   68
B.   64
C.   56
D.   78
Question #3
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant / A / B / C / D Order Accurate / 17 / 8 / 5 / 55 Order Not Accurate / 46 / 53 / 40 / 26 If three different orders are selected, find the probability that they are all from restaurant B. Assume that the orders are selected with replacement. Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   1.25
B.   1.45
C.   1.15
D.   1.39
Question #4
Assuming boys and girls are equally likely, find the probability of a couple's last child being a baby boy. They have a total of 6 children not including the last child in question and all were boys before the last child was born. Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   50
B.   60
C.   45
D.   40
Question #5
A sample of 2 different calculators is randomly selected from a group containing 5 that are defective and 14 that have no defects. Assume that the sample is taken with replacement. What is the probability that at least one of the calculators is defective? Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   43.44
B.   39.27
C.   45.71
D.   46.89
Question #6
In the town of Maplewood a certain type of DVD player is sold at just two stores. 77% of the sales are from store A and the rest of the sales are from store B. 4% of the DVD players sold at store A are defective while 3% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A? Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   83.5
B.   81.1
C.   79.3
D.   81.7
Question #7
How many ways can 3 people be chosen and arranged in a straight line if there are 12 people to choose from?
A.   1,190
B.   1,330
C.   1,320
D.   1,510
Question #8
The library is to be given 7 books as a gift. The books will be selected from a list of 12 titles. If each book selected must have a different title, how many possible selections are there?
A.   736
B.   792
C.   765
D.   784
Question #9
Find the missing value required to create a probability distribution, then find the standard deviation for the given probability distribution. Round to the nearest hundredth. x / P(x) 0 / 0.05 1 / 2 / 0.2 3 / 0.16 4 / 0.17
A.   1.68
B.   1.11
C.   1.72
D.   1.21
Question #10
A 28-year-old man pays $209 for a one-year life insurance policy with coverage of $13,024. If the probability that he will live through the year is 0.993, what is the expected value for the insurance policy? Round to the nearest cent.
A.   -137.58
B.   -127.33
C.   -109.77
D.   -117.83
Question #11
According to a college survey, 84% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 219 (rounded to the nearest hundredth).
A.   6.75
B.   5.08
C.   5.48
D.   5.43
Question #12
An archer is able to hit the bull's-eye 28% of the time. If she shoots 11 arrows, what is the probability that she gets exactly 5 bull's-eyes? Assume each shot is independent of the others. Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   13.91
B.   12.09
C.   11.88
D.   11.08
Question #13
The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 4. Find the probability that in a randomly selected year, the number of lightning strikes is 1. Express your answer as a percentage rounded to the nearest hundredth.
A.   7.11
B.   7.33
C.   9.55
D.   6.66
Question #14
Suppose the probability of contracting a certain disease is 1 in 61 for a new case in a given year. Approximate the probability that in a town of 105 people there will be at least one new case of the disease next year. Express your answer as a percentage rounded to the nearest hundredth without the % sign.
A.   85.14
B.   80.16
C.   82.12
D.   84.13
Question #15
A statistics student plans to use a TI-84 Plus calculator on her final exam. From past experience, she estimates there is a 98% probability that the calculator will work on any given day. Because the final exam is so important, she plans to bring in two calculators in case one loses power. Does she gain much by bringing in the backup calculator? Calculate the probability that she will be able to complete her exam with a working calculator. (Express your answer as a percent rounded to the nearest hundredth without the % sign.)
A.   99.96
B.   99.25
C.   99.33
D.   98.46
Question #16
Draw the standard normal distribution. Shade the area between the z-score of -3.02 and -1.46. Find the shaded area. Round to the nearest ten-thousandth.
A.   0.0721
B.   0.0699
C.   0.0709
D.   0.0803
Question #17
Draw the standard normal distribution. The shaded area to the left of the z-score is 0.3707. Find the z-score. Round to the nearest hundredth.
A.   -0.41
B.   -0.39
C.   -0.33
D.   -0.28
Question #18
Suppose that replacement times for washing machines are normally distributed with a mean of 9 years and a standard deviation of 2.7 years. Find the replacement time that separates the top 1.7% from the rest. Round to the nearest hundredth.
A.   15.76
B.   14.72
C.   13.22
D.   15.14
Question #19
The weights of the fish in a certain lake are normally distributed with a mean of 8 lb and a standard deviation of 2 lb. If 15 fish are randomly selected, what is the probability that the mean weight will be more than 8.2 lb? Express the answer as a percentage rounded to the nearest hundredth without the % sign.
A.   33.63
B.   32.67
C.   34.83
D.   36.84
Question #20
Approximate the probability that in 48 tosses of a fair die, more than 13 fives will be obtained. Express the probability as a decimal rounded to the nearest thousandth.
A.   0.021
B.   0.017
C.   0.026
D.   0.014

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