Question

A sample of restaurants in a city showed that the average cost of a glass of iced tea is $1.25 with a a standard

deviation of 7c. Three of the restaurants charge 95¢, 1.00, and $1.35. Determine the z-value for each restaurant.

Answer 1

For the restaurant that charges 95 cents, the z-score is -4.29.

For the restaurant that charges $1, the z-score is -3.57.

For the restaurant that charges $1.35, the z-score is 1.43

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average cost of a glass of iced tea is $1.25 with a standard deviation of 7c.

This means that
`\mu = 1.25, \sigma = 0.07`

Restaurant that charges 95 cents:

The z-score is found when X = 0.95. So

`Z = (X - \mu)/(\sigma)`

`Z = (0.95 - 1.25)/(0.07)`

`Z = -4.29`

For the restaurant that charges 95 cents, the z-score is -4.29.

Restaurant that charges $1:.

X = 1

`Z = (X - \mu)/(\sigma)`

`Z = (1 - 1.25)/(0.07)`

`Z = -3.57`

For the restaurant that charges $1, the z-score is -3.57.

Restaurant that charges $1.35:

X = 1.35

`Z = (X - \mu)/(\sigma)`

`Z = (1.35 - 1.25)/(0.07)`

`Z = 1.43`

For the restaurant that charges $1.35, the z-score is 1.43