Question

Fill in the blank. In a drive thru performance study, the average service time for McDonald's is 198.46 seconds with a standard deviation of 5.71 seconds. A random sample of 78 times is taken. There is a 63% chance that the average drive-thru service time is less than ________ seconds.

1) 198.25

2) 196.57

3) 200.35

4) There is not enough information to determine this.

5) 198.67

Answer 1

Given, = 198.46 , = 5.71  

Using central limit theorem,

P( < x) = P(Z < x - / ( / sqrt(n) ))

So,

We have to calculate such that P( < x) = 0.63

P(Z < x - / ( / sqrt(n) )) = 0.63

From Z table, z-score for the probability of 0.63 is 0.3319

x - / ( / sqrt(n) ) = 0.3319

x - 198.46 / (5.71 / sqrt(78) ) = 0.3319

Solve for x

X = 198.67