The national survey has conducted a poll examining the financial health of public servants as they...

The national survey has conducted 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.

1. 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. here define a binominal random variable and interpret what this means in terms of the scenario given in the question.

2. Find the probability that more than 5 people who responded are adequately prepared for retirement. This will help you plan for future hiring. Please use the binomial probability formula and show each step manually while calculating. Secondly, interpret the result you got related to the context of the question. Here I am not only assessing you for getting the right answer/number but also your ability to interpret the answer in a given situation.

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Expert Solution

1.Let X be the number of persons who feel adequately prepared for retirement. It is well known that X follows Binomial distribution with parameters n and p. Here n is the number of persons in the random sample and here n=10. And also a person of age 55 years and over is prepared for retirement with probability 0.6. Hence the number of people who feel adequately prepared for retirement can be distributed as follows.

2. Probability that more than 5 people who responded are adequately prepared for retirement is obtained as follows.

From the random sample, it is observed that more than half of the people of age 55 and above are prepared for retirement with probability 0.63. That means, proposed changes to mandatory retirement laws are not appreciated half of the people in approximately 63% of the cases.

orchestra answered 1 year ago

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