Questions: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.3 years, and standard deviation of 0.6 years. If you randomly pGirchase one item, what is the probability it will last longer than 12 years? Round answer to three decimal places

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.3 years, and standard deviation of 0.6 years. If you randomly pGirchase one item, what is the probability it will last longer than 12 years? Round answer to three decimal places
Transcript text: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.3 years, and standard deviation of 0.6 years. If you randomly pGirchase one item, what is the probability it will last longer than 12 years? Round answer to three decimal places
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Solution

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Solution Steps

Step 1: Calculate the Z-score for the individual item

Using the formula $Z = \frac{X - \mu}{\sigma}$, where $X = 12$, $\mu = 11.3$, and $\sigma = 0.6$, we find that $Z = 1.167$.

Final Answer:

The probability that the variable exceeds 12 is approximately 0.122.

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