Awebsite advertises job openings on its website, but job seekers have to pay to access the list of job openings. the website recently completed a survey to estimate the number of days it takes to find a new job using its service. it took the last 30 customers an average of 60 days to find a job. assume the population standard deviation is 10 days. construct a 90% confidence interval of the population mean number of days it takes to find a job.

The 90% confidence interval would be given by (57.006;62.994)  

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

represent the sample mean  

population mean (variable of interest)  

represent the population standard deviation  

n=30 represent the sample size  

Assuming the X follows a normal distribution  

The sample mean is distributed on this way:

The confidence interval on this case is given by:

(1)

The next step would be find the value of , , and  

Using the normal standard table, excel or a calculator we see that:  

Since we have all the values we can replace:

So on this case the 90% confidence interval would be given by (57.006;62.994)  

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.