1.The probability that a car will have a flat tire while driving through a certa
ID: 3131499 • Letter: 1
Question
1.The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005. Use the Poisson distribution to approximate the probability that among 14,000 cars passing through this tunnel, exactly two will have a flat tire.
0.8783
0.1947
0.1460
D.
0.1217
2.According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.
4.0
2.8
3.5
D.
0.2
3. Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 53 times, keeping track of the "fives" rolled.
Not binomial: there are too many trials.
Procedure results in a binomial distribution.
Not binomial: the trials are not independent.
Not binomial: there are more than two outcomes for each trial.
4. Use the given values of n and p to find the minimum usual value - 2 and the maximum usual value + 2. n = 1205, p = 0.98.
Min: 1171.18; Max: 1190.62
Min: 1190.62; Max: 1171.18
Min: 1174.03; Max: 1187.77
Min: 1176.04; Max: 1185.76
5. Identify the given random variable as being discrete or continuous. The cost of a randomly selected orange.
Continuous.
Discrete.
6. Suppose that random guesses are made for 5 questions on a multiple-choice test (n = 5). Suppose that there are 5 different options to choose from for each problem (p = 0.20). Using a binomial distribution, what is the probability that the number of correct scores is exactly 3?
0.5421
0.1257
0.0512
0.2435
7. Determine whether the following is a probability distribution. In a certain town, 40% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree.
x
P(x)
0
0.0992
1
0.3456
2
0.3456
3
0.1536
4
0.056
This is not a probability distribution.
This is a probability distribution.
8. Suppose that 20% of students have an A in a particular class. Assume that 5 people from the class are randomly polled. What is the probability that exactly one of them has an A?
0.200
0.591
0.450
0.410
9. If one of your exams is a multile choice test with 4 possible answers (A, B, C, D) to each problem, and 10 problems total. If you randomly guess, what is the probability that you will get 8 or more correct?
0.0012
0.0004
0.0034
0.0056
10.If z is a standard normal variable, find the probability P(z < 0.97).
0.8078
0.8340
0.1660
0.8315
11. In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.
0.2881
0.3791
0.0910
0.1971
12. A normal quartile plot is given below for the lifetimes (in hours) of a sample of batteries of a particular brand. Use the plot to assess the normality of the lifetimes of these batteries.
The data is not normally distributed.
The data is normally distributed.
13. If z is a standard normal variable, find the probability P(-0.73 < z < 2.27).
1.54
0.2211
0.4884
0.7557
14. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170 and 220.
0.0703
0.3811
0.2257
0.1554
15. Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483.
0.3264
0.13
0.6736
-0.13
16. Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.0694.
1.26
1.39
1.45
1.48
17. Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
0.8708
0.8485
0.1292
0.8907
18. The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?
0.4834
0.0179
0.9834
0.0166
19. If z is a standard normal variable, find the probability that z lies between 0.7 and 1.98.
0.2175
0.2181
-0.2181
1.7341
20. In a population of 210 women, the heights of the women are normally distributed with a mean of 64.4 inches and a standard deviation of 2.9 inches. If 36 women are selected at random, find the mean (mu sub x-bar) and standard deviation (sigma sub x-bar) of the population of sample means. Assume that the sampling is done without replacement and use a finite population correction factor.
64.4 inches, 0.44 inches
64.4 inches, 2.07 inches
64.4 inches, 2.9 inches
58.8 inches, 2.65 inches
A.0.8783
B.0.1947
C.0.1460
D.
0.1217
Explanation / Answer
1.
Here, p = 0.00005 and n =14000.
Note that the probability of x successes is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = n p = 14000*0.0005 = 0.7
x = the number of successes = 2
Thus, the probability is
P ( 2 ) = 0.121663399 [ANSWER, D]
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2.
As
u = mean = n p
and n = 16, p = 0.22, then
u = 16*0.22 = 3.52 [ANSWER, C]
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