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Solved: Constructing and Graphing Binomial Distributions
Chapter 4, Problem 24E(choose chapter or problem)
Problem 24E
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.
Messy Desk Thirty-eight percent of hiring managers have a negative view of workers with a messy desk. You randomly select 10 hiring managers and ask them whether they have a negative view of workers with a messy desk. The random variable represents the number of hiring managers who have a negative view of workers with a messy desk.
Questions & Answers
QUESTION:
Problem 24E
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.
Messy Desk Thirty-eight percent of hiring managers have a negative view of workers with a messy desk. You randomly select 10 hiring managers and ask them whether they have a negative view of workers with a messy desk. The random variable represents the number of hiring managers who have a negative view of workers with a messy desk.
ANSWER:
Solution:
Step 1 of 3:
From the given problem, we have
n = 10, p = 38%
= 0.38
The pmf of a Binomial distribution is
P(X = x) = ; x = 0, 1, 2,...., n.
Where, X represents the number of hiring managers who have a negative view of workers with a messy desk.
a). Here we have to construct a binomial distribution.
Given, n = 10, p = 0.38
Where,
..= 10) is obtained from excel by using the function:
“=Binomdist(x, n, p, false)”.
That is,
x |
P(x) |
0 |
0.0084 |
1 |
0.0514 |
2 |
0.1419 |
3 |
0.2319 |
4 |
0.2487 |
5 |
0.1829 |
6 |
0.0934 |
7 |
0.0327 |
8 |
0.0075 |
9 |
0.0010 |
10 |
0.000062 |