In a survey on the quality of customer service at Car Toys, customers were asked

Question

In a survey on the quality of customer service at Car Toys, customers were asked to rate the service on a scale from 1 to 10 with 10 being that a customer was completely satisfied with the service. Assume that the distribution of responses can be approximated by a normal distribution with a mean of 7 and a standard deviation of 1.

a. What is the probability that an individual customer gives a rating of at least 8?

b. In a random sample of 10, what is the probability that the average rating is at least 8?

Explanation / Answer

Mean is 7 and standard deviation s is 1, z is given as (x-mean)/s

a) P(x>8) =P(z>(8-7)/1)=P(z>1) or 1-P(z<1), using normal distribution table we get 1-0.8413=0.1587

b) P(xbar>8)=P(z>(8-7)/(1/sqrt(10)))=P(z>3.16) or 1-P(z<3.16) =0 because P(z<3.16) is nearly 1

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