# How many 60-year old females on average will be living at age 61?

**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 25^{th} 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

- What scores fall between –1 and +1 standard deviation?
- What percent of all scores fall between –1 and +1 standard deviation?
- What score falls at +2 standard deviations?
- 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?

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

- 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:

- 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?

- 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 |