In a manufacturing process, a machine produces bolts that have an average length of 3 inches with a variance of. 03. If we randomly select three bolts from this process, what is the probability the mean length of the bolt is "at most 3.1 inches"

Answer: 0.8413

Step-by-step explanation:

population mean = 3

population variance = 0.03

sd (standard deviation) = √0.03

Let x = sample mean

x has a mean of 3 and sd of √0.03/√3 = √0.01 = 0.1

And we can aprox the sample mean distribution using a normal distribution

Note: this approximation maybe is not so good (n = 3)

with mean = 3 and sd = 0.1

z = (x-3) / 0.1 has a standard normal distribution

P (x<3.1) = P (z< (3.1-3) / 0.1) = P (z<1) = 0.8413