Question

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

Answer 1

Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.

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
`\bar X` = sample mean diameter

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

Z =
`( \bar X-\mu)/((\sigma)/(√(n) ) ) }` ~ N(0,1)

where,
`\mu` = population mean diameter = 141 millimetres

`\sigma` = 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(
`\bar X` > 141.4 millimetres)

P(
`\bar X` > 141.4) = P(
`( \bar X-\mu)/((\sigma)/(√(n) ) ) }` >
`(141.4-141)/((7)/(√(39) ) ) }` ) = P(Z > 0.36) = 1 - P(Z
`\leq` 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.