Econ 3

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E270 HW3

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20
z is the standard normal random variable.
1 P(z < 1.35) = _______.
a 0.0735
b 0.9115
c 0.1056
d 0.1251
2 P(z > 1.45) = _______.
a 0.9265
b 0.7412
c 0.1103
d 0.0735
3 P(0.00 < z < 1.55)
a 0.9394
b 0.6576
c 0.4394
d 0.3515
4 P(-1.76 < z < 1.76) = _______.
a 0.9522
b 0.9426
c 0.9216
d 0.8812
5 In a normal distribution the fraction of data points falling within ±1.25 standard deviations from the mean is _______.
a 0.8530
b 0.8230
c 0.7888
d 0.7498
6 In a normal distribution the fraction of data points falling within ±2 standard deviations from the mean is _______.
a 0.9756
b 0.9544
c 0.9372
d 0.9298
7 In a normal distribution the proportion of data points falling within ±3 standard deviations from the mean is _______.
a 0.9974
b 0.9775
c 0.9579
d 0.9387
8 The middle 85% of z scores in a standard normal distribution fall within the interval ______ and ______.
a -1.44 1.44
b -1.46 1.46
c -1.48 1.48
d -1.50 1.50
9 The middle 98% of z scores fall within the interval ______ and ______.
a -2.29 2.29
b -2.31 2.31
c -2.33 2.33
d -2.35 2.35
Next FOUR questions (10-13) are based on the following information
The mileage of Greatyear tires is normally distributed with a mean μ = 57,000 miles and a standard deviation of σ = 6000 miles.
10 What fraction of Greatyear tires can be expected to last more than 65,000 miles?
a 0.1221
b 0.1110
c 0.1009
d 0.0918
11 The fraction of tires expected to last between 47000 and 67000 miles is _______.
a 0.9050
b 0.8688
c 0.8340
d 0.8007
12 The middle interval that includes the mileage of 95% of all tires is,
P(x₁ < x < x₂) = 0.95
a 48,360 65,640
b 47,160 66,840
c 45,240 68,760
d 43,020 70,980
13 Greatyear is considering a guarantee that will provide a discount on replacement tires if the original tires do not reach the guaranteed mileage. What should the guarantee mileage be if Greatyear wants no more than (at most) 3 percent of the tires be eligible for the discount guarantee?
a 47,160
b 46,500
c 45,720
d 44,700
Next FOUR questions (14-17) are based on the following information
Young people, ages 13-24, spend an average of μ = 20.1 hours a week online. Assume the time spent online has a normal distribution with a standard deviation of σ = 5.75 hours a week.
14 By how many standard deviations 28 hours spent online deviates from the mean?
a 1.25
b 1.31
c 1.37
d 1.45
15 The fraction of young people who spend more than 28 hours a week online is,
a 0.1335
b 0.1151
c 0.1093
d 0.0853
16 The amount of time spent online by what fraction of young people fall within ±7 hours from the population mean?
a 0.8064
b 0.7776
c 0.7416
d 0.7016
17 The middle 95% of young people spend between ______ and ______ hours a week online.
a 6.7 33.5
b 8.8 31.4
c 10.7 29.5
d 12.7 27.5
18 Ten percent (10%) of American workers spend over 31 hours online at work during a working week. Assume the standard deviation is 6 hours. What is the average number of hours spent online per working week at work?
a 22.3
b 23.3
c 24.3
d 25.3
Next TWO questions are based on the following information
The U.S. Bureau of Labor Statistics reports that the average annual expenditure on food for all families in 2013 was $6,900. Assume that annual expenditure on food is normally distributed with a standard deviation σ = $1,850.
19 What proportion of food expenditures is within ±3,000 from the mean expenditure?
a 0.8324
b 0.8714
c 0.8948
d 0.9250
20 Among the families, 10% of them spent above $_______.
a $9,268
b $9,509
c $9,934
d $10,526
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