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Ch. 6.1 #7-49 odd

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15. Waiting to Be Seated The average waiting time to be seated for dinner at a popular restaurant is<br />

23.5 minutes, with a standard deviation of 3.6 minutes. Assume the variable is normally distributed.<br />

When a patron arrives at the restaurant for dinner, find the probability that the patron will have to wait the<br />

following time.<br />

a) Between 15 and 22 minutes<br />

X 15 23.5 8.5<br />

z 2.36<br />

3.6 3.6<br />

X 22 23.5 1.5<br />

z 0.42<br />

3.6 3.6<br />

P( 2.36 z 0.42) 0.3372 0.0091 0.3281<br />

-2.36 -0.42<br />

b) Less than 18 minutes or more than 25 minutes<br />

X 18 23.5 5.5<br />

z 1.53<br />

3.6 3.6<br />

X <br />

25 23.5 1.5<br />

z 0.42<br />

3.6 3.6<br />

P( z 1.53 or z 0.42) 0.0630 (1 0.6628) 0.063 0.3372 0.4002<br />

-1.53 0.42<br />

c) Is it likely that a person will be seated in less than 15 minutes?<br />

X 15 23.5 8.5<br />

z 2.36<br />

3.6 3.6<br />

Pz ( 2.36) 0.0091

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