Question

Please solve all parts for upvote

At work some business analysts estimate that the length of time people work at a job has a mean of 6.2 years and a standard deviation of 4.5 years

a) Explain why you suspect this distribution may be skewed to the right.

b) If you take a random sample of 5 people, can you use Table Z to find the probability they work at their current job for at least 10 years? Explain in context.

Now consider a random sample of 50 people.

c) Will the assumptions for the central limit theorem hold? Explain in the context of the question.

Independence Assumption:

Randomization condition:

10% (big population) condition:

Normal Population Assumption:

as shown in part (a), the length of time people have worked for the same company would not follow a normal distribution so we need to check the sample size assumption.

Sample size assumption:

Large enough sample condition:

d) What are the mean and standard deviation for the length of time at a job in a sample of 50 people? Show your work for any calculations.

e) Using the 68-95-99.7 rule, between what two values would the middle 95% of values for the length of time at a job fall?

f) If we were to take a random sample of 75 people, would the interval containing the middle 68% of values be wider or narrower than the one found in part (e)? Explain.

Answer 1

(a)

Some people will work more than other people. That is some people has work length larger than other. That is there may be some high outliers.

Hence, distribution should be skewed to right.

(b)

Since distribution of skewed to right and sample size is less than 30 so we cannot apply CLT. That is we we cannot assume sampling distribution is symmetric.

(c)

Independence Assumption: Yes

Randomization condition: Yes

10% (big population) condition: Yes

Normal Population Assumption: Yes

Sample size is greater than 30 so assumptions about sample size has been fullfilled.

Sample size assumption: Yes

Large enough sample condition: Yes

d)

The mean is:

The standard deviation is

e)

The required interval is:

f)

Now we have

The interval containing the middle 68% is

This interval is narrower than interval found in part (e).