Cost of Personal ComputersThe average price of a personal

Chapter 6, Problem 21E

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QUESTION:

The average price of a personal computer (PC) is $949. If the computer prices are approximately normally distributed and \(\sigma=\$ 100\), what is the probability that a randomly selected PC costs more than $1200? The least expensive 10% of personal computers cost less than what amount?

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QUESTION:

The average price of a personal computer (PC) is $949. If the computer prices are approximately normally distributed and \(\sigma=\$ 100\), what is the probability that a randomly selected PC costs more than $1200? The least expensive 10% of personal computers cost less than what amount?

ANSWER:

Step 1 of 2

From the given problem we have 

The mean \(\mu=949\)

The standard deviation \(\sigma=100\)

Here we have to find the probability that a randomly selected PC costs more than $1200. 

Thus, 

\(\begin{aligned} P(X>1200) & =1-P\left(Z<\frac{X-\mu}{\sigma}\right) \\ = & 1-P\left(Z<\frac{1200-949}{100}\right) \\ = & 1-P(Z<2.51) \\ = & 1-0.9940 \\ = & 0.0060 \end{aligned}\)

Hence, the probability that a randomly selected PC costs more than $1200 is 0.006.

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