Question

40​% of employees judge their peers by the cleanliness of their workspaces. You randomly select 8 employees and ask them whether they judge their peers by the cleanliness of their workspaces. The random variable represents the number of employees who judge their peers by the cleanliness of their workspaces.

P(x)
0
1
2
3
4
5
6
7
8

Required:
Consturct a histogram and describe its shape.

Answer 1

See attachment and explanation below

It's is a bell shaped histogram

Explanation:

This is a binomial distribution problem.

A binomial distribution is a distribution whose experiment has two possible outcomes, a success and failure. The outcomes of the experiment do not depend on each other.

For n trials in a binomial distribution, the probability of getting success:

P(X=x) = n!/[(n-x)!x!] × p^x × q^(n-x)

Where p = success

q = failure

n = 8, p= 40% = 0.4

q = 1-0.4 = 0.6

See attachment for workings and histogram diagram.

From the diagram, the shape of the histogram is bell shaped. It is also known as a normal distribution.