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A manufacturer knows that their items have a normally distributed length, with a mean of 18.2 inches, and standard deviation of 4.8 inches one is chosen at random , what is the probability that it is less than 28.6 inches long?

Respuesta :

To find the corresponding probability, first we need to convert our value to a z-score using the following formula:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula in our problem, we have:

[tex]z=\frac{28.6-18.2}{4.8}\approx2.08[/tex]

Then, checking the corresponding probability in a z-table, we have:

[tex]P(z\leq2.08)=0.9812[/tex]

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