**Answer:**

**Step-by-step explanation:**

Hello!

Be the variable of interest:

X: Number of weeks it takes a worker aged 55 plus to find a job

Sample average X[bar]= 22 weeks

Sample standard deviation S= 11.89 weeks

Sample size n= 40

a)

The point estimate of the population mean is the sample mean

X[bar]= 22 weeks

It takes on average 22 weeks for a worker aged 55 plus to find a job.

b)

To estimate the population mean using a confidence interval, assuming the variable has a normal distribution is

X[bar] ± *

The structure of the interval is "point estimate" ± "margin of error"

d= * = 2.023*= 3.803

c)

The interval can be calculated as:

[22 ± 3.803]

[18.197; 25.803]

Using s 95% confidence level, you'd expect the population mean of the time it takes a worker 55 plus to find a job will be within the interval [18.197; 25.803] weeks.

d)

Job Search Time (Weeks)

21
, 14, 51, 16, 17, 14, 16, 12, 48, 0, 27, 17, 32, 24, 12, 10, 52, 21, 26, 14, 13, 24, 19
, 28
, 26
, 26, 10, 21, 44, 36, 22, 39, 17, 17, 10, 19, 16, 22, 5, 22

To study the form of the distribution I've used the raw data to create a histogram of the distribution. See attachment.

As you can see in the histogram the distribution grows gradually and then it falls abruptly. The distribution is right skewed.