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A manufacturer knows that their items have a normally distributed length, with a mean of 8.4 inches, and standard deviation of 1.4 inches.If one item is chosen at random, what is the probability that it is less than 11.8 inches long?

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We will make use of the z-score to calculate the probability. The z-score is calculated using the formula:


z=(x-\mu)/(\sigma)

where x is the score, μ is the mean, and σ is the standard deviation.

From the question, we have the following parameters:


\begin{gathered} x=11.8 \\ \mu=8.4 \\ \sigma=1.4 \end{gathered}

Therefore, we have the z-score to be:


\begin{gathered} z=(11.8-8.4)/(1.4) \\ z=2.43 \end{gathered}

Using a calculator, we can get the probability value to be:


P=0.9925

The probability is 0.9925 or 99.25%.

A manufacturer knows that their items have a normally distributed length, with a mean-example-1
User Alexandre Rondeau
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