Question

A survey reported that 37% of people plan to spend more on eating out after they retire. If

eight people are randomly​ selected, determine the values below.

a.	The expected number of people who plan to spend more on eating out after they retire
b.	The standard deviation of the individuals who plan to spend more on eating out after they retire
c.	The probability that two or fewer in the sample indicate that they actually plan to spend more on eating out after retirement

Answer 1

Solution:

Given:

p = probability of people plan to spend more on eating out after they retire = 0.37

n = sample size = Number of people  randomly​ selected = 8

Part a)

The expected number of people who plan to spend more on eating out after they retire

x = Number of people who plan to spend more on eating out after they retire follows a Binomial distribution with parameters n =8 and p = 0.37

Thus mean or expected value for Binomial distribution is given by:

Thus the expected number of people who plan to spend more on eating out after they retire =

Part b)

The standard deviation of the individuals who plan to spend more on eating out after they retire

Part c)

The probability that two or fewer in the sample indicate that they actually plan to spend more on eating out after retirement

That is find:  

Using Binomial probability formula:

Where

and q = 1- p = 1 - 0.37 = 0.63

Thus

and

Thus

Thus the probability that two or fewer in the sample indicate that they actually plan to spend more on eating out after retirement is 0.3811.