Probability- Normal Distribution Question- Need Help Understanding

Question

A manufacturer knows that their items have a normally distributed length, with a mean of 16.8 inches, and standard deviation of 1 inches.

If one item is chosen at random, what is the probability that it is less than 19.6 inches long? (Give answer to 4 decimal places.)

Answer 1

let x = length of item

we want to find P(x < 19.6) for N(16.8,1), which is a non-standard normal distribution.

To find that probability we need to convert above inequality to standard normal distribution: N(0,1), so we can utilize standard normal probability table.

This is done by translating x to z-statistic = (x - mean)/std, so above inequality becomes:

P ( z < (19.6 - 16.8)/1) = P(z < 2.8) = 0.9974