Question

plz help
The lifespan of radios is normally distributed with μ=15.2 years, σ=5 years. Kelly's beloved radio is 25 years old and she is now wondering whether or not it's in the top 5% of the oldest radios today. What would be the lower limit for the oldest 5%?

Answer 1

Suppose \(X\) is the random variable for a radio's age. We want to find the cutoff age \(k\) that gives \(P(X>k)=0.05\).

Transform to the standard normal random variable \(Z\):
\[P\left(\frac{X-15.2}{5}>\frac{k-15.2}{5}\right)=P\left(Z>\frac{k-15.2}{5}\right)=0.05\]
We know that \(P(Z>1.645)=0.05\), which means you set the two expressions equal to each other and solve for \(k\):
\[\frac{k-15.2}{5}=1.645~~\iff~~k=23.425\]
Since \(25>k\), the radio is indeed in the top 5%.

Answer 2

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