Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 125125 millimeters, and a variance of 4949. If a random sample of 4141 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 2.22.2 millimeters? Round your answer to four decimal places.

The probability that the sample mean would differ from the population mean by greater than 2.2 millimeters is 0.0222.

Step-by-step explanation:

Let X = the diameter of steel bolts.

The population mean diameter of steel bolts is, μ = 125 mm and the population variance is, σ² = 49 mm.

A random sample of n = 41 steel bolts are selected.

According to the Central limit theorem, if a large sample (n > 30) is selected from an unknown population with mean μ and variance σ² then the sampling distribution of sample mean follows a Normal distribution with mean, and variance, .

Compute the probability that the sample mean differ from the population mean by greater than 2.2 mm as follows:

*Use a z-table for the probability.

Thus, the probability that the sample mean would differ from the population mean by greater than 2.2 millimeters is 0.0222.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!