Questions: The manager of a fast-food restaurant records each day for a year the amount of money received from sales of food that day. Using software, he finds a mean of 1165 and a standard deviation of 220. a) Today's sale is 1800. Calculate the z-score. Round to 2 decimal places (A) -2.89 (B) 2.89 (C) 3.26 (D) -2.12

Solution Steps

To calculate the $z$-score, we use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \( X \) is the value of today's sale, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. Plug in the given values and compute the $z$-score.

We are given:

• \( X = 1800 \)
• \( \mu = 1165 \)
• \( \sigma = 220 \)

The formula for the $z$-score is: \[ z = \frac{X - \mu}{\sigma} \]

Substituting the values, we get: \[ z = \frac{1800 - 1165}{220} \]

\[ z = \frac{635}{220} \approx 2.8864 \]

\[ z \approx 2.89 \]

Final Answer