Question

The national surveyconducted a poll examining the financial health of public servants as they approach retirement age. According to responses from the survey of persons 55 years of age and over, 60% of them have stated that they are adequately prepared for retirement. Proposed changes to mandatory retirement laws may mean that persons who would normally be retiring at age 65, may no longer choose to do so, particularly if they feel they are not financially in the position to. Based on the findings of this survey, you want to extrapolate the number of people in your division who are adequately prepared for retirement. To do so, a random and independent sample of employees ages 55 plus where n=10 was conducted. a) Define the random variable x as the number of persons who feel adequately prepared for retirement. We know that x is a binomial random variable. Please write a paragraph explaining what random varioable x means in the given context. Use graphs, number or whatever is required to answer the question. It can be about a page long.

b) Find the probability that more than 5 people who responded are adequately prepared for retirement. This will help you plan for future hiring. Please calculate and also mention the logic and reason behind it while answering.

Answer 1

(a) The random variable x represents the number of people in the division who are adequately prepared for retirement.

The binomial distribution graph is:

The binomial distribution is:

	10	n
	0.6	p
		cumulative
X	P(X)	probability
0	0.00010	0.00010
1	0.00157	0.00168
2	0.01062	0.01229
3	0.04247	0.05476
4	0.11148	0.16624
5	0.20066	0.36690
6	0.25082	0.61772
7	0.21499	0.83271
8	0.12093	0.95364
9	0.04031	0.99395
10	0.00605	1.00000
	1.00000
	6.000	expected value
	2.400	variance
	1.549	standard deviation

(b) The probability that more than 5 people who responded are adequately prepared for retirement is 0.6331.