Question

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 2.82.8 and a mean diameter of 210 inches. If 84 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.3 inches? Round your answer to four decimal places.

Answer 1

Answer:  0.2322   or    23.22 %

Step-by-step explanation:

We have to solve and find the area out of these limits

 μ + 0,3 =  210 + 0,3   ⇒    210,3  and

 μ - 0,3  =  210 - 0,3   ⇒    209.7

z(l)   = ( x - 210 ) / (2.8/√84)   ⇒  z(l) =  - (0.3 * 9,17)/ 2.8

z (l)  = - 1.195  

We need to interpole from z table

                1.19         ⇒     0.1170

               1.20       ⇒      0.1151

    Δ  ⇒     0.01     ⇒      0.0019

And between our point   1,195 and 1,19   the difference is  0.005

then        0.01          ⇒   0.0019

               0.005      ⇒      ?? (x)

we find x =  0.00095

to get the area for poin  z (l)  - 1.195 up to final left tail is from  z table

0,1170 - 0.00095 =  0.1161

And by symmetry  to the right is the same

So   0.1161 * 2   =  0.2322

We find the area out of the above indicated limits  the area we were looking for. This is the probability of finding shafts over and below the population mean and 0.3 inches