Caelan

## Answered question

2021-08-21

According to a market research firm, 52% of all residential telephone numbers in Los Angeles are unlisted.
A telephone sales firm uses random digit dialing equipment that dials residential numbers at random, whether or not they are listed in the telephone directory.
The firm calls 500 numbers in Los Angeles.
What is the probability that at least half the numbers dialed are unlisted? (Remember to check that you can use the Normal approximation.)

### Answer & Explanation

Clara Reese

Skilled2021-08-22Added 120 answers

The z-score is the value decreased by the mean, divided by the standard deviation: $z=\frac{x-\mu }{\sigma }=\frac{0.50-0.52}{0.0223}\approx -0.90$ Determine the corresponding probability using table A: $P\left(X>0.50\right)=P\left(Z\succ 0.90\right)=1-P\left(Z<-0.90\right)=1-0.1841=0.8159$

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