Question

A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 10.2 inches, and standard deviation of 3.3 inches.

If 48 items are chosen at random, what is the probability that their mean length is greater than 8.8 inches?

(Round answer to four decimal places)

Answer 1

Answer: Hope this helps ;)

Explanation:

The probability that the mean length of 48 items is greater than 8.8 inches can be calculated using the normal distribution.

First, we need to standardize the value 8.8 inches by subtracting the mean length (10.2 inches) and dividing by the standard deviation (3.3 inches):

(8.8 - 10.2) / 3.3 = -1.4 / 3.3 = -0.42424242

We can use a z-table or a normal distribution calculator to find the probability that a random variable is less than -0.42424242 standard deviations below the mean. This probability is equal to the probability that the mean length of 48 items is greater than 8.8 inches.

Using a calculator, we find that the probability is 0.3389.

Rounding to four decimal places, the probability that the mean length of 48 items is greater than 8.8 inches is 0.3389.