Answer:
Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.
Step-by-step explanation:
We are given that Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimetres, and a standard deviation of 7. 
A random sample of 39 steel bolts is selected.
Let  = <u><em>sample mean diameter</em></u>
 = <u><em>sample mean diameter</em></u>
The z score probability distribution for sample mean is given by;
                             Z  =   ~ N(0,1)
  ~ N(0,1)
where,  = population mean diameter = 141 millimetres
 = population mean diameter = 141 millimetres
             = standard deviation = 7 millimetres
 = standard deviation = 7 millimetres
            n = sample of steel bolts = 39
Now, Percentage the sample mean would be greater than 141.4 millimetres is given by = P( > 141.4 millimetres)
 > 141.4 millimetres)
       P( > 141.4) = P(
 > 141.4) = P(  >
 >  ) = P(Z > 0.36) = 1 - P(Z
 ) = P(Z > 0.36) = 1 - P(Z  0.36)
 0.36)
                                                             = 1 - 0.6406 = <u>0.3594</u>
The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.