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Cost of Personal ComputersThe average price of a personal
Chapter 6, Problem 21E(choose chapter or problem)
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?
Questions & Answers
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.