Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimeters, and a standard deviation of 7. If a random sample of 39 steel bolts is selected, what is the probability that the sample mean would be greater than 141.4 millimeters

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 = sample mean diameter

The z score probability distribution for sample mean is given by;

                            Z  =    ~ N(0,1)

where, = population mean diameter = 141 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)

      P( > 141.4) = P( > ) = P(Z > 0.36) = 1 - P(Z 0.36)

                                                            = 1 - 0.6406 = 0.3594

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.