Question

a coffee shop recorded the number of customers per day over a period of one year. the mean number of customers was 95, and the standard deviation is 30. if 145 customers came into the coffee shop on labor day, which of the following statements is true? select the correct answer below: the number of customers who came into the coffee shop on labor day is 3 standard deviations to the right of the mean. the number of customers who came into the coffee shop on labor day is 5 standard deviations to the left of the mean. the number of customers who came into the coffee shop on labor day is within 2 standard deviations to the right of the mean. the number of customers who came into the coffee shop on labor day is 4 standard deviations to the right of the mean.

Explanation:

Step1: Calculate the difference from the mean

We find the difference between the number of customers on Labor Day (145) and the mean (95). So, \( 145 - 95 = 50 \).

Step2: Relate the difference to standard deviation

The standard deviation is 30. We check how many standard deviations 50 is from the mean. We can calculate the number of standard deviations \( z=\frac{145 - 95}{30}=\frac{50}{30}\approx1.67 \). Since \( 1.67<2 \), the number of customers on Labor Day is within 2 standard deviations to the right of the mean.

Answer:

The number of customers who came into the coffee shop on Labor Day is within 2 standard deviations to the right of the mean.