Problem 22E

Using a Distribution to Find Probabilities In Exercise, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Breaking Up Twenty-nine percent of Americans ages 16 to 21 years old say that they would break up with their boyfriend or girlfriend for $10,000. You randomly select seven 16- to 21-year-olds. Find the probability that the number of 16- to 21-year-olds who say that they would break up with their boyfriend or girlfriend for $10,000 is (a) exactly two, (b) more than three, and (c) between one and four, inclusive.

Answer

Step 1 of 1

(a)

We are asked to find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution.

Then determine whether the events are unusual.

If convenient, use a table or technology to find the probabilities.

We have given 29% of Americans ages 16 to 21 years old say that they would break up with their boyfriend or girlfriend for $10,000.

You randomly select seven 16 to 21 years old.

We are asked to find the probabilities that the number of 16 to 21 years old who say that they would break up with their boyfriend or girlfriend for $10,000.

- Exactly two,
- More than three,
- Between one and four, inclusive.

The probability distribution would be the binomial distribution since the experiment has a fixed number n of independent trials.

A binomial distribution represented by the following formula,

Where

We need to find the exactly two

We need to find more than three

We need to find between one and four, inclusive

Since the value of probabilities are not less than 0.05, hence there are no events which are unusual.

Using Minitab, we can find the probabilities.

We need to find the exactly two

Steps to find out the pdf of the Binomial distribution.

- Go to menu Calc under that select sub menu probability distributions.
- Under probability distributions select a Binomial.
- Click on radio button probability and enter the relevant data.

We need to find the exactly two

We need to find between one and four, inclusive

(x) |
P(X=x) |

1 |
0.260044 |

2 |
0.318645 |

3 |
0.216918 |

4 |
0.0886 |