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

Answer 1

Answer:

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

Step-by-step explanation:

Z-score:

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

$Z = \frac{X - \mu}{\sigma}$

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

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.95 - 1.25}{0.07}$

$Z = -4.29$

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

Restaurant that charges $1:.

X = 1

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1 - 1.25}{0.07}$

$Z = -3.57$

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

Restaurant that charges $1.35:

X = 1.35

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1.35 - 1.25}{0.07}$

$Z = 1.43$

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