Solution Found!
Constructing and Graphing Binomial Distributions In
Chapter 4, Problem 23E(choose chapter or problem)
Problem 23E
Constructing and Graphing Binomial Distributions In Exercise, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning.
100th Birthday Sixty-seven percent of adults ages 55 and older want to reach their 100th birthday. You randomly select seven adults ages 55 and older and ask them whether they want to reach their 100th birthday. The random variable represents the number of adults ages 55 and older who want to reach their 100th birthday.
Questions & Answers
QUESTION:
Problem 23E
Constructing and Graphing Binomial Distributions In Exercise, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning.
100th Birthday Sixty-seven percent of adults ages 55 and older want to reach their 100th birthday. You randomly select seven adults ages 55 and older and ask them whether they want to reach their 100th birthday. The random variable represents the number of adults ages 55 and older who want to reach their 100th birthday.
ANSWER:
Solution:
Step 1 of 3:
From the given problem, we have
n = 7, p = 67%
= 0.67
The pmf of a Binomial distribution is
P(X = x) = ; x = 0, 1, 2,...., n.
Where, X represents the number of adults age 55 and older who want to reach their 100th birthday.
a). Here we have to construct a binomial distribution.
Given, n = 7, p = 0.67
Where, is obtained from excel by using the function:
“=Binomdist(x, n, p, false)”.
That is,
x |
P(x) |
0 |
0.0004 |
1 |
0.0061 |
2 |
0.0369 |
3 |
0.1248 |
4 |
0.2535 |
5 |
0.3088 |
6 |
0.209 |
7 |
0.0606 |