Answer:
A 98% confidence interval for the mean assembly time is [21.34, 26.49]
.
Step-by-step explanation:
We are given that a sample of 40 times yielded an average time of 23.92 minutes, with a sample standard deviation of 6.72 minutes.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
                                P.Q. =   ~
  ~ 
where,  = sample average time = 23.92 minutes
 = sample average time = 23.92 minutes
              s = sample standard deviation = 6.72 minutes
              n = sample of times = 40
               = population mean assembly time
 = population mean assembly time
<em>
Here for constructing a 98% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
</em>
<u>So, a 98% confidence interval for the population mean, </u> <u> is;
</u>
<u> is;
</u>
P(-2.426 <  < 2.426) = 0.98  {As the critical value of z at 1%  level
 < 2.426) = 0.98  {As the critical value of z at 1%  level
                                                of significance are -2.426 & 2.426}   
P(-2.426 <  < 2.426) = 0.98
 < 2.426) = 0.98
P(  <
 <  <
 <  ) = 0.98
 ) = 0.98
P(  <
 <  <
 <  ) = 0.98
 ) = 0.98
<u>98% confidence interval for</u>  = [
 = [  ,
 ,  ]
 ]
                                      = [  ,
 ,  ]
 ]  
                                     = [21.34, 26.49]
Therefore, a 98% confidence interval for the mean assembly time is [21.34, 26.49]
.