Suppose the local Best Buy store averages 483 customers per day entering the facility with a standard deviation of 112 customers. A random sample of 48 business days was selected. What is the probability that the average number of customers in the sample is between 480 and 500?
A)0.2521
B)0.4284
C)0.1579
D)0.3377

Question

Quizplus · Accepted Answer

The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, if the sample size is large enough. In this case, the sample size is 48, which is large enough to apply the central limit theorem.The mean of the sample means will be equal to the mean of the population, which is 483. The standard deviation of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is 112 / sqrt(48) = 16.Therefore, the probability that the average number of customers in the sample is between 480 and 500 is:P(480 < X < 500) = P((480 - 483) / 16 < Z < (500 - 483) / 16) = P(-1.875 < Z < 1.0625) = 0.2521

Suppose the Local Best Buy Store Averages 483 Customers Per