QUESTIONS
Question 1
An automobile manufacturer is concerned about the possibility of a fault in the engine of a particular model of one of its cars. This fault could potentially cause the engine to fail to start. The average number of cars per year that experience this fault is 3 cars. If the probability that 8 or more cars experience this fault in a year is greater than 0.05, the company will issue a recall. Will the company issue a recall for this engine fault? Use Excel to find the probability.
Question 2
The state department of transportation is coordinating road crews to fix potholes after a particularly snowy winter. Initial estimates gave an average of 7.8 potholes per mile of highway. Find the probability that there are 11 or more potholes in a randomly selected one-mile stretch of highway. Use Excel to find the probability.
- Round your answer to three decimal places.
Question 3
In a recent baseball season, Ron was hit by pitches 21 times in 602 plate appearances during the regular season. Assume that the probability that Ron gets hit by a pitch is the same in the playoffs as it is during the regular season. In the first playoff series, Ron has 23 plate appearances. What is the probability that Ron will get hit by a pitch exactly once? Use Excel to find the probability.
- Round your answer to three decimal places.
Question 4
To see if a spinner that is divided into 100 equal sections labeled 1 to 100 is fair, a researcher spins the spinner 1000 times and records the result. Let X represent the outcome. The table below shows the probability distribution of the data. Find the mean and the standard deviation of the probability distribution using Excel.
- Round the mean and standard deviation to two decimal places.
“x” P(x)
1 0.011
2 0.011
3 0.011
4 0.01
5 0.008
6 0.011
7 0.011
8 0.01
9 0.01
10 0.011
11 0.011
12 0.01
13 0.008
14 0.01
15 0.008
16 0.012
17 0.006
18 0.011
19 0.012
20 0.009
21 0.011
22 0.012
23 0.01
24 0.011
25 0.011
26 0.01
27 0.01
28 0.01
29 0.012
30 0.009
31 0.011
32 0.011
33 0.008
34 0.009
35 0.009
36 0.009
37 0.01
38 0.008
39 0.009
40 0.01
41 0.012
42 0.01
43 0.009
44 0.009
45 0.01
46 0.011
47 0.01
48 0.011
49 0.011
50 0.011
51 0.011
52 0.01
53 0.007
54 0.011
55 0.009
56 0.01
57 0.007
58 0.011
59 0.011
60 0.012
61 0.008
62 0.011
63 0.009
64 0.01
65 0.01
66 0.011
67 0.009
68 0.01
69 0.01
70 0.009
71 0.01
72 0.01
73 0.011
74 0.008
75 0.009
76 0.009
77 0.011
78 0.011
79 0.011
80 0.009
81 0.01
82 0.008
83 0.009
84 0.011
85 0.012
86 0.01
87 0.009
88 0.011
89 0.01
90 0.01
91 0.009
92 0.011
93 0.011
94 0.011
95 0.008
96 0.01
97 0.01
98 0.01
99 0.011
100 0.009
Question 5
A database system assigns a 32-character ID to each record, where each character is either a number from 0 to 9 or a letter from A to F. Assume that each number or letter being selected is equally likely. Find the probability that at least 20 characters in the ID are numbers. Use Excel to find the probability.
- Round your answer to three decimal places.
Question 6
A study randomly selected 100 samples, each of which consisted of 100 people, and recorded the number of left-handed people, X. The table below shows the probability distribution of the data. Find the mean and the standard deviation of the probability distribution using Excel.
- Round the mean and standard deviation to two decimal places.
x P(x)
1 0.01
2 0.01
3 0.04
4 0.02
5 0.02
6 0.09
7 0.08
8 0.04
9 0.07
10 0.02
11 0.04
12 0.04
13 0.16
14 0.08
15 0.08
16 0.02
17 0.02
18 0.08
19 0.04
20 0.04
Question 7
A roulette wheel has 38 slots, numbered 1 to 36, with two additional green slots labeled 0 and 00. Jim, a dealer at a roulette table, tests the roulette wheel by spinning a ball around the wheel repeatedly and seeing where the ball lands. The ball has an equally likely chance of landing in each slot. If Jim spins the ball around the wheel 25 times, what is the probability that the ball lands in a green slot at most twice? Use Excel to find the probability.
- Round your answer to three decimal places.
Question 8
At a certain fast food restaurant, 77.5% of the customers order items from the value menu. If 14 customers are randomly selected, what is the probability that at least 9 customers ordered an item from the value menu? Use Excel to find the probability.
- Round your answer to three decimal places.
Question 9
In a 40-year period, a city’s official weather station recorded 78 snowstorms with at least 12 inches of total snow accumulation. Assume that this pattern follows a Poisson distribution. Find the probability that the city’s weather station records exactly 4 snowstorms with at least 12 inches of total snow accumulation for one randomly selected year in the period. Use Excel to find the probability.
- Round your answer to three decimal places.
Question 10
An insurance company is assessing the risk of selling flood insurance. Under the company’s policies, if a customer lives in an area where they have a greater than 5% chance of experiencing 4 or more floods in 10 years, the customer must pay a higher premium. Drew lives in an area where the average number of floods per 10 years is 1.6 floods. Will Drew have to pay the higher premium for flood insurance? Use Excel to find the probability.
Question 11
An insurance office records the number of claims received each day, X, and built the probability distribution table below using the data collected. Find the mean and the standard deviation of the probability distribution using Excel.
- Round the mean and standard deviation to two decimal places.
x P(x)
0 0.2016
1 0.1218
2 0.1214
3 0.0729
4 0.0667
5 0.0586
6 0.0556
7 0.0515
8 0.0427
9 0.0397
10 0.0351
11 0.0265
12 0.0229
13 0.0185
14 0.0163
15 0.0137
16 0.0126
17 0.0087
18 0.0052
19 0.0051
20 0.0029
Question 12
A survey asked recently retired people the number of people, X, they met through work during their working lives that they considered close friends. The table below is a probability distribution table representing the data collected. Find the mean and the standard deviation of the probability distribution using Excel.
- Round the mean and standard deviation to three decimal places.
x P(x)
1 0.009
2 0.066
3 0.098
4 0.12
5 0.065
6 0.065
7 0.064
8 0.06
9 0.054
10 0.05
11 0.048
12 0.045
13 0.045
14 0.041
15 0.037
16 0.03
17 0.022
18 0.02
19 0.019
20 0.016
21 0.012
22 0.012
23 0.002
ANSWERS:
Question 1
An automobile manufacturer is concerned about the possibility of a fault in the engine of a particular model of one of its cars. This fault could potentially cause the engine to fail to start. The average number of cars per year that experience this fault is 3 cars. If the probability that 8 or more cars experience this fault in a year is greater than 0.05, the company will issue a recall. Will the company issue a recall for this engine fault? Use Excel to find the probability.
Answer:
The company will not issue a recall because the probability is less than 0.05.
Question 2
The state department of transportation is coordinating road crews to fix potholes after a particularly snowy winter. Initial estimates gave an average of 7.8 potholes per mile of highway. Find the probability that there are 11 or more potholes in a randomly selected one-mile stretch of highway. Use Excel to find the probability.
- Round your answer to three decimal places.
Answer:
0.165
Question 3
In a recent baseball season, Ron was hit by pitches 21 times in 602 plate appearances during the regular season. Assume that the probability that Ron gets hit by a pitch is the same in the playoffs as it is during the regular season. In the first playoff series, Ron has 23 plate appearances. What is the probability that Ron will get hit by a pitch exactly once? Use Excel to find the probability.
- Round your answer to three decimal places.
Answer:
0.367
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