m distribution rough The me required for housekeeping o clean a hotel room or th

Question

m distribution rough The me required for housekeeping o clean a hotel room or the next customer varies between 30 and 50 minutes and follows he continuous un a) Calculate the value of fx). f(x)-| | (Type an integer or decimal rounded to three decimal places as needed.) b) What are the mean and standard deviation for this distribution? The mean of this distribution is minutes. Type an integer or decimal rounded to two decimal places as needed) The standard deviation of this distribution isminutes. omplete parts a (Type an integer or decimal rounded to two decimal places as needed.) c) What is the probability that the next room will require exactly 42 minutes to clean? (Type an integer or decimal rounded to three decimal places as needed.) d) What is the probability that the next room will require less than 35 minutes to clean? (Type an integer or decimal rounded to three decimal places as needed.) e) What is the probability that the next room will require more than 41 minutes to clean? (Type an integer or decimal rounded to three decimal places as needed.)

Explanation / Answer

Answers to all problems here:

a. f(x) = x-30 / 50-30 = (x-30)/20

b. Mean = (a+b)/2 = 30+50 /2 = 40
Stdev = (b-a)/sqrt(12) = (50-30)/sqrt(12) = 5.77

c. P(X=42) = 1/(50-30) = 1/20 = .05

d. P(X<35) = (35-30)/50-30 = 5/20 = .25

e. P(X>41) = (b-x)/b-a = (50-41)/50-30 = 9/20 = .45

f. P(33<X<45) = (x-y)/b-a = (45-33)/50-30 = .60

g. P(X=c) = .80
So, c - a / b-a = .80
(c-30)/(50-30) = .8
c = .8*20+30= 46.0

Answer is 46 minutes

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