Question

1. a shopper went to a sale and bought a dvd player for $242. the mean price for this dvd player at all stores in the area was $280 with a standard deviation of $26. another shopper bought a tv for $486 that has a mean price of $548 with a standard deviation of $46. use the z - score to compare these two sales. which item is the better deal?

Explanation:

Step1: Calculate z - score for DVD player

The formula for z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the observed value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For the DVD player, \(x = 242\), \(\mu=280\), \(\sigma = 26\)
\(z_{DVD}=\frac{242 - 280}{26}=\frac{- 38}{26}\approx - 1.46\)

Step2: Calculate z - score for TV

For the TV, \(x = 486\), \(\mu = 548\), \(\sigma=46\)
\(z_{TV}=\frac{486-548}{46}=\frac{-62}{46}\approx - 1.35\)

Answer:

Since \(-1.46<-1.35\) (the DVD player has a more negative z - score), the DVD player is the better deal.