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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.)

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..SOLUTION

[tex]\begin{gathered} Mean=6.1 \\ Standard\text{ deviation=0.5} \end{gathered}[/tex][tex]\begin{gathered} Z-score=\frac{x-mean}{standard\text{ deviation}}=\frac{6-6.1}{0.5}=-0.2 \\ \end{gathered}[/tex]

The normal curve is given below.

Using statistical table, the probability is given as;

[tex]0.4207[/tex]

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