Question

A manufacturer knows that their items have a normally distributed length, with a mean of 6.1 inches, and standard deviation of 0.5 inches.If one item is chosen at random, what is the probability that it is less than 6 inches long? (Give answer to 4 decimal places.)

Answer 1

..SOLUTION

`\begin{gathered} Mean=6.1 \\ Standard\text{ deviation=0.5} \end{gathered}`
`\begin{gathered} Z-score=\frac{x-mean}{standard\text{ deviation}}=(6-6.1)/(0.5)=-0.2 \\ \end{gathered}`

The normal curve is given below.

Using statistical table, the probability is given as;

`0.4207`