Question

A screw manufacturer makes specialized tiny screws that are 15mm long. The manufacturing process does not make every screw exactly 15mm long. The lengths of the screws are normally distributed with mean 15mm and standard deviation 0.04mm. To test for quality control, 36 screws are to be measured. What is the probability that a sample mean is less than 14.99mm?

Answer 1

Answer:

The probability that a sample mean is less than 14.99mm=0.066808

Step-by-step explanation:

We are given that

Mean,$\mu=15 mm$

Standard deviation,$\sigma=0.04 mm$

n=36

We have to find the probability that a sample mean is less than 14.99mm.

We know that

$P(\bar{x}<a)=P(Z<\frac{\bar{x}-a}{\frac{\sigma}{\sqrt{n}}})$

Using the formula

$P(\bar{x}<14.99)=P(Z<\frac{14.99-15}{\frac{0.04}{\sqrt{36}}})$

$P(\bar{x}<14.99)=P(Z<-1.5)$

=$1-P(Z\geq -1.5)$

$=1-0.93319$

=0.066808

Hence,  the probability that a sample mean is less than 14.99mm=0.066808