500 câu trắc nghiệm Kinh tế lượng – 5C
List the different possible samples, and find the mean of each of them.
11) Personal phone calls received in the last three days by a new employee were 4, 1, and 3. Assume that samples of size 2 are randomly selected with replacement from this population of three values.
Possible samples: 4-4; 4-1; 4-3; 1-4; 1-1; 1-3; 3-4; 3-1; 3-3 Means: 4, 2.5, 3.5, 2.5, 1, 2, 3.5, 2, 3
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
12) 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 40 different applicants are randomly selected, find the probability that their mean is above 215.
○ 0.1179
● 0.0287
○ 0.3821
○ 0.4713
13) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6
hours.
○ 0.0036
○ 0.0103
○ 0.0008
● 0.0025
14) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than 71.
● 0.8962
○ 0.9012
○ 0.5036
○ 0.0008
15) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 109 inches, and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25 randomly picked years will exceed 111.8 inches?
○ 0.5808
● 0.0808
○ 0.0026
○ 0.4192
For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation.
16) n = 33 and p = .9
● Normal approximation is not suitable.
○ Normal approximation is suitable.
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
17) In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.
○ 0.0420
○ 0.8962
● 0.1038
○ 0.3962
Use the normal distribution to approximate the desired probability.
18) Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time. Find the probability that among the 60 trains, 38 or fewer arrive on time. Based on the result, does it seem plausible that the “on-time” rate of 74% could be correct?
○ .0316 , yes
● .0409 , no
○ .0409 , yes
○ .0316 , no
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Examine the given data set and determine whether the requirement of a normal distribution is satisfied. Assume that the requirement for a normal distribution is loose in the sense that the population distribution need not be exactly normal, but it must have a distribution which is basically symmetric with only one mode. Explain why you do or do not think that the requirement is satisfied.
19) The amount of rainfall (in inches) in 25 consecutive years in a certain city.
20.4 25.1 22.8 27.0 23.5
24.2 26.0 25.6 23.3 24.1
21.9 27.6 24.7 25.3 21.6
31.0 23.6 26.1 25.5 24.8
18.1 22.4 24.9 30.0 29.3
The requirement for normality is satisfied since a histogram of the data is roughly bell shaped; it is roughly symmetric with a single mode.
Solve the problem.
20) A normal probability 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. Explain your reasoning.
Since the normal probability plot displays curvature, it appears that lifetimes of these batteries are probably not normally distributed.