Question

A manufacturer knows that their items have a normally distributed length, with a mean of 9.1 inches, and standard deviation of 1.4 inches.

If one item is chosen at random, what is the probability that it is less than 8.5 inches long?

Answer 1

First, we will need to find the Z-Score

where X = Required Probability, = mean, = standard deviation

Therefore, Substituting the Values,

z = -0.42857

Further, We will look-up a Standard Z-Table and find the Area Corresponding to this value

Since we have been asked Probability of being Less than 8.5 inches, so we need P(X<Z)

From any standard Z-Table, we can find this to be:

P(X < Z) = 0.33412

This means the Probability that it will be less than 8.5 inches is 0.33412

i.e. 33.412% will be less than 8.5 inches.

Please UpVote. It Helps. Thank You