Question

Suppose the local Best Buy store averages 480 customers per day entering the facility with a standard deviation of 110 customers. A random sample of 48 business days was selected. What is the probability that the average number of customers in the sample is less than 500

Answer 1

The probability that the average number of customers in the sample is less than 500

P(x≤500) = 0.1038

Explanation:

Step(i):-

Given average of customers per day 'μ' = 480

Standard deviation of customers 'σ' = 110

Given sample size 'n' = 48

Let x = 500

`Z = (x-mean)/(S.D) = (480-500)/((110)/(√(48) ) ) = -1.260`

Step(ii):-

The probability that the average number of customers in the sample is less than 500

P(x≤500) = P(z≤-1.26)

= 0.5 - A(1.26)

= 0.5 -0.3962

= 0.1038

Conclusion:-

The probability that the average number of customers in the sample is less than 500 = 0.1038