Questions: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.6 years, and standard deviation of 1.2 years. If you randomly purchase one item, what is the probability it will last longer than 3 years? Round answer to three decimal places.

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.6 years, and standard deviation of 1.2 years. If you randomly purchase one item, what is the probability it will last longer than 3 years? Round answer to three decimal places.
Transcript text: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.6 years, and standard deviation of 1.2 years. If you randomly purchase one item, what is the probability it will last longer than 3 years? Round answer to three decimal places $\square$
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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 $X = 3$, $\mu = 3.6$, and $\sigma = 1.2$, we find that $Z = -0.5$.

Final Answer:

The probability that the variable exceeds 3 is approximately 0.691.

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