Question

statistics notes 7.2 standard normal distributions
robert scott
example
a pizza parlor franchise specifies that the mean amount of cheese on a large pizza should be 8 ounces and the standard deviation is only 0.5 ounces. an inspector picks out a large pizza at random in one of the pizza parlors & finds that it is made with 6.9 ounces of cheese. assume that the amount of cheese on a pizza follows a normal distribution. if the amount of cheese is below the mean by more than 3 standard deviations, the parlor will be in danger of losing its franchise.
how many standard deviations from the mean is 6.9? is the pizza parlor in danger of losing its franchise?
$$ z = \frac { x - \mu } { \sigma } $$

Explanation:

Step1: Identify the values

Given \(x = 6.9\), \(\mu=8\), \(\sigma = 0.5\)

Step2: Calculate the z - score

Use the formula \(z=\frac{x-\mu}{\sigma}\)
Substitute the values: \(z=\frac{6.9 - 8}{0.5}=\frac{-1.1}{0.5}=- 2.2\)

Step3: Compare with the critical value

The critical value is \(z=-3\) (since we are looking at values below the mean). Since \(-2.2>-3\)

Answer:

The amount of cheese \(6.9\) ounces is \(2.2\) standard deviations from the mean. The pizza parlor is not in danger of losing its franchise.