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StatisticsQ&A LibraryState Populations. From Infoplease, we obtained data on state population from which we constructed the following frequency distribution.Population size (millions)FrequencyUnder 161–under 282–under 363–under 585–under 101510&over7Compute the following conditional probabilities directly; that is, do not use the conditional probability rule. For a state selected at random, find the probability that the population of the state obtained isa. between 2 million and 3 million.b. between 2 million and 3 million given that it is at least 1 million.c. less than 5 million given that it is at least 1 million.d. Interpret your answers in parts (a)–(c) in terms of percentages.Question

Asked Jan 11, 2020

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**State Populations.** From Infoplease, we obtained data on state population from which we constructed the following frequency distribution.

Population size (millions) | Frequency |

Under 1 | 6 |

1–under 2 | 8 |

2–under 3 | 6 |

3–under 5 | 8 |

5–under 10 | 15 |

10&over | 7 |

Compute the following conditional probabilities directly; that is, do not use the conditional probability rule. For a state selected at random, find the probability that the population of the state obtained is

a. between 2 million and 3 million.

b. between 2 million and 3 million given that it is at least 1 million.

c. less than 5 million given that it is at least 1 million.

d. Interpret your answers in parts (a)–(c) in terms of percentages.

Step 1

(a)

The probability of an event can be obtained as follows:

Step 2

Here, the event that the population of the state obtained is between 2 million and 3 million. And frequency of the event is 6. And total frequency is 50.

Substitute 6 for “Number of ways event occurs” and 50 for total frequency” in the above equation

The probability of the event can be obtained as shown below:

Step 3

Thus, the probability that the population of the state obtained is between 2 million and 3 million is 0.12.

(b)

Here, the event *E* denote that that the population of the state obtained is between 2 million and 3 million given that it is at least 1 million. There are 44 (8+6+8+15+7=44) states that population of 1 m...

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