Suppose that the length of time waiting in line for the drive through at Wendy’s

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)

Explanation / Answer

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

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