# Stats 1

Data File 3

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Chapter Five

1)    If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

2)    The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?

3)    The amount of Jen’s monthly phone bill is normally distributed with a mean of \$60 and a standard deviation of \$12.  Fill in the blanks:

68% of her phone bills are between \$______________ and \$______________.

4)    The amount of Jen’s monthly phone bill is normally distributed with a mean of \$50 and a standard deviation of \$10.  Find the 25th percentile.

5)    The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches.  What percentage of bolts will have a diameter greater than 0.32 inches?

6)    The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?

7)    A final exam in Statistics has a mean of 73 with a standard deviation of 7.73.  Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?

8)    A mean score on a standardized test is 50 with a standard deviation of 10. Answer the following

a.     What scores fall between –1 and +1 standard deviation?

b.     What percent of all scores fall between –1 and +1 standard deviation?

c.     What score falls at +2 standard deviations?

d.     What percentage of scores falls between +1 and +2 standard deviations?

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Chapter Six

1)    For the following questions, would the following be considered “significant” if its probability is less than or equal to 0.05?

a.     Is it “significant” to get a 12 when a pair of dice is rolled?

b.     Assume that a study of 500 randomly selected school bus routes showed that 480 arrived on time.  Is it “significant” for a school bus to arrive late?

2)    If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. What is the probability of getting at least one head?

3)    A sample space consists of 64 separate events that are equally likely.  What is the probability of each?

4)    A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles.  If a marble is randomly selected from the bag, what is the probability that it is blue?

5)    The data set represents the income levels of the members of a country club.  Estimate the probability that a randomly selected member earns at least \$98,000.

112,000            126,000            90,000                        133,000            94,000

112,000            98,000                        82,000                        147,000            182,000

86,000                        105,000            140,000            94,000                        126,000

119,000            98,000                        154,000            78,000                        119,000

6)    Suppose you have an extremely unfair coin:  The probability of a head is ¼ and the probability of a tail is ¾.  If you toss the coin 32 times, how many heads do you expect to see?

7)    The following table is from the Social Security Actuarial Tables.  For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of that age.  Determine the following using the table:

a.     To what age may a female of age 60 expected to live on the average?  To what age is a male of age 70 expected to live on average?

b.     How many 60-year old females on average will be living at age 61?  How many 70-year old males on average will be living at age 71?

MALES                                                            FEMALES

Age

P(Death within one year)

Number of Living

Life Expectancy

P(Death within one year)

Number of Living

Life Expectancy

10

0.000111

99,021

65.13

0.000105

99,217

70.22

20

0.001287

98,451

55.46

0.000469

98,950

60.40

30

0.001375

97,113

46.16

0.000627

98,431

50.69

40

0.002542

95,427

36.88

0.001498

97,513

41.11

50

0.005696

91,853

28.09

0.003240

95,378

31.91

60

0.012263

84,692

20.00

0.007740

90,847

23.21

70

0.028904

70,214

12.98

0.018938

80,583

15.45

80

0.071687

44,272

7.43

0.049527

594,31

9.00

90

0.188644

12,862

3.68

0.146696

24,331

4.45