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

Answer:

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

  P(x≤500) = 0.1038

Step-by-step 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

$Z = \frac{x-mean}{S.D} = \frac{480-500}{\frac{110}{\sqrt{48} } } = -1.260$

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