Kinh tế lượngTrắc nghiệm

500 câu trắc nghiệm Kinh tế lượng – 4C

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
11) Choosing 4 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time without replacement, keeping track of the number of red marbles chosen.
○ Not binomial: there are too many trials.
○ Not binomial: there are more than two outcomes for each trial.
● Not binomial: the trials are not independent.
○ Procedure results in a binomial distribution.

Answer the question.
12) Suppose that a law enforcement group studying traffic violations determines that the
accompanying table describes the probability distribution for five randomly selected people, where x is the number that have received a speeding ticket in the last 2 years. Is it unusual to find no speeders among five randomly selected people?

x Px
0 0.08
1 0.18
2 0.25
3 0.22
4 0.19
5 0.08

● No
○ Yes

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
13) n = 64, x = 3, p = 0.04
○ 0.375
○ 0.139
○ 0.091
● 0.221

Find the indicated probability.
14) A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 12 drivers living on one particular street, 3 were involved in a car accident last year. If 12 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?
● 0.0866
○ 0.9314
○ 0.4091
○ 0.0686

Find the standard deviation, \(\sigma \), for the binomial distribution which has the stated values of n and p. Round
your answer to the nearest hundredth.
15) n = 40; p = 3/5
● \(\sigma \) = 3.10
○ \(\sigma \) = 0.69
○ \(\sigma \) = 6.37
○ \(\sigma \) = 7.22

Use the given values of n and p to find the minimum usual value \(\mu – 2\sigma \) and the maximum usual value \(\mu + 2\sigma \).
16) n = 107, p = 0.23
● Minimum: 15.9; maximum: 33.32
○ Minimum: 33.32; maximum: 15.9
○ Minimum: -13.29; maximum: 62.51
○ Minimum: 20.26; maximum: 28.96

Solve the problem.
17) A company manufactures batteries in batches of 8 and there is a 3% rate of defects. Find the mean number of defects per batch.
○ 0.232
○ 0.248
● 0.24
○ 7.76

18) In a certain town, 50% of voters favor a given ballot measure. For groups of 22 voters, find the variance for the number who favor the measure.
○ 2.35
● 5.50
○ 11.00
○ 30.25

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more
than 2 standard deviations. That is, unusual values are either less than \(\mu – 2\sigma \) or greater than \(\mu + 2\sigma \).
19) According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to “Eyewitness News” at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be unusual to find that 990 of the 2500 televisions are tuned to “Eyewitness News”?
○ No
● Yes

Use the Poisson Distribution to find the indicated probability.
20) A mountain search and rescue team receives an average of \(\mu \) = 0.71 calls per day. Find the probability that on a randomly selected day, they will receive fewer than two calls.
● 0.8407
○ 0.3491
○ 0.1593
○ 0.1239

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