Question

question
at a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 14 minutes and a standard deviation of 3 minutes. if you visit that restaurant 31 times this year, what is the expected number of times that you would expect to wait between 16 minutes and 22 minutes, to the nearest whole number?

Explanation:

Step1: Calculate z-scores for 16,22

For $x=16$: $z_1=\frac{16-14}{3}=\frac{2}{3}\approx0.67$
For $x=22$: $z_2=\frac{22-14}{3}=\frac{8}{3}\approx2.67$

Step2: Find corresponding probabilities

From z-table: $P(Z<0.67)\approx0.7486$, $P(Z<2.67)\approx0.9962$

Step3: Compute interval probability

$P(0.67

Step4: Calculate expected visits

$31\times0.2476\approx7.6756$

Step5: Round to nearest whole number

Round $7.6756$ to 8

Answer:

8