The 2008 Workplace Productivity Survey, commissioned by LexisNexis and prepared by World One Research, included the question, "How many hours do you work at your job on a typical workday." Let x = the number of hours a legal professional works on a typical workday. Suppose that x is normally distributed with a known standard deviation of 12.6. A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours. Use the sample information to estimate μ, the mean number of hours a legal professional works on a typical workday. Develop a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday.

A 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

Step-by-step explanation:

We are given that x is normally distributed with a known standard deviation of 12.6.

A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                               P.Q.  =    ~ N(0,1)

where, = sample average mean response = 9 hours

              = population standard deviation = 12.6

            n = sample of legal professionals = 250

             = mean number of hours a legal professional works

Here for constructing a 95% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < < 1.96) = 0.95

P( < < ) = 0.95

P( < < ) = 0.95

95% confidence interval for = [ , ]

                                       = [ , ]

                                       = [7.44 hours, 10.56 hours]

Therefore, a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

the least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9