Question

Suppose that the length of time waiting in line for the drive through at Wendy’s is approximately normally distributed with a mean time of 136 seconds and a standard deviation of 29 seconds. Suppose on your most recent visit to Wendy’s you waited 3 minutes, (180 seconds).

a. Show what is being asked on the diagram below. Label the horizontal axis with 136, 180 and x.  


b. Calculate your Z-score. Show your z-score on the diagram.







c. Interpret the Z-score. (3 things)






d. What percentage of people would wait between 107 and 194 seconds? Show what is being asked on the diagram below.

(Hint: Find the Z-scores first)

Answer 1

Given

mean=136 seconds

sd=29 seconds

x=180 seconds

we know z=(x-mean)/sd

Therefore at x=136 seconds=mean

we have z=0

for x=180 secons

z=(180-136)/29=1.517=1.52

We say that the z score implies that it is 1.52 standard deviations away from the mean

A z score of 1.52 also means that atleast 90% of the data points are around the mean

d) z=(107-136)/29=-1

z=(194-136)/29=2

ie we are interested in -1<z<2

We know 1 standard deviation has 65% of the data

2 standard deviations has 95% of the data

3 standard deviations has 99.99% of the data

16.67% +2*16.67%=50% of the data is covered

Area under the curve for -1 <z<2 =50%=0.5