Question

A company manufactures a large number of rods. The lengths of the rods are normally distributed with a mean length of 4.4 inches and a standard deviation of .5 inches. If you choose a rod at random, what is the probability that the rod you chose will be greater than 4.0 inches

Answer 1

0.78814

Explanation:

We solve using z score

z = (x-μ)/σ, where

x is the raw score = 4.0 inches

μ is the population mean = 4.4 inches

σ is the population standard deviation = 0.5 inches

z = 4.0 - 4.4/0.5

z = -0.8

Probability value from Z-Table:

P(x<4.0) = 0.21186

P(x>4.0) = 1 - P(x<4.0)

= 1 - 2.1186

= 0.78814

The probability that the rod you chose will be greater than 4.0 inches is 0.78814.