6.33 The time required for housekeeping to clean a hotel roonm for the next cust

Question

6.33 The time required for housekeeping to clean a hotel roonm for the next customer varies between 25 and 45 minutes and follows the continuous uniform distribution. a. Calculate the value of f(x) b. What are the mean and standard deviation for this c. What is the probability that the next room will require d. What is the probability that the next room will require e. What is the probability that the next room will require f. What is the probability that the next room will require g. What time represents the 70th percentile of this distribution? exactly 30 minutes to clean? less than 32 minutes to clean? more than 36 minutes to clean? between 28 and 34 minutes to clean? distribution?

Explanation / Answer

a)for uniform distribution f(x) =1/(b-a) =1/(45-25)=1/20

b) mean =(a+b)/2 =(45+25)/2=35

std deviation =(b-a)/(12)1/2 =(45-25)/(12)1/2 =5.7735

c) probability of cleaning the room will require exactly 30 minutes =P(X=30) =0 ( as in a continuous distribution probability is area under the curve for given values. here for under a point area is equal to 0)

d) P(X<32) =(32-25)/(45-25) =7/20 =0.35

e)P(X>36)=(45-36)/(45-25)=9/20=0.45

f)P(28<X<34) =(34-28)/(45-25)=6/20=0.30

g)70th percentile corresponding value =25+0.7*(45-25)=39

please revert for any clarification required,

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