Please help me with this Stats question!

Question

A manufacturer knows that their items have a normally distributed length, with a mean of 6.3 inches, and standard deviation of 1.4 inches.

If one item is chosen at random, what is the probability that it is less than 5.3 inches long?

Answer 1

Since we are dealing with a normally distributed variable, we will be using a z-score to determine the probability.

z-score for normally distributed variable x = (x - mean)/standard deviation.

For x = 5.3 and given mean and standard deviation, z-score = (5.3 - 6.3)/1.4 = -0.72

Use standard normal probability table or calculator to determine probability (z < -0.72) = 0.236