Suppose the local Best Buy store averages 522customers every day entering the facility with a standard deviation of 124 customers.A random sample of 40 business days was selected.What is the probability that the average number of customers in the sample is between 530 and 540?
A) 0.2387
B) 0.1621
C) 0.3057
D) 0.0572

Question

Quizplus · Accepted Answer

We first need to standardize the sample mean using the formula z = (x̄ - μ) / (σ / √n), where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. 
Plugging in the values, we get: 
z = (540 - 522) / (124 / √40) = 1.32 
z = (530 - 522) / (124 / √40) = 0.51 
Using a standard normal distribution table or calculator, we find the area to the right of 1.32 is 0.0934, and the area to the right of 0.51 is 0.1949. 
To find the area between the two z-scores, we can subtract the area to the right of 1.32 from the area to the right of 0.51: 
0.0934 - 0.1949 = 0.1015 
Since this is the probability of getting a sample mean between 530 and 540, the answer is B) 0.1621.

Suppose the Local Best Buy Store Averages 522customers Every Day