Question

A service department at a dealership calculates the average cost of service done at their department to be $1000 with a standard deviation of $200. What is the probability the total service cost of 80 vehicles is less than $81.000?A)0.5B)0.71C)0.29D)The sample size is too small to compute the probability of the total

Answer 1

First of all, we must realize that the probability of the total service being under $81.000 is equal to the probability of the average cost of each one the 80 service being 1012.5

In order to proceed, we use the formula adjusted for the population size (80) in order to get the intended Z value yielding:

Z=(1012.5-1000)/(200/sqrt(80))=0.56

Checking in the table for the probability for this particular Z value gives us 0.21226 (i.e. the probaility of the average being between 1000 and 1012.5), nontheless we must add the probability of it being under 1000, which is precisely 0.5

Ading the probabilities gives us that the total probablity for the average cost of a service from among the 80 choosen is:

0.5+0.21226=0.71226

Rounding to the nearest hundredths gives us P=0.71