The time required to prepare a certain specialty ooffee at a local coffee shop i

Question

The time required to prepare a certain specialty ooffee at a local coffee shop is uniformly distributed between 35 and 55 seconds. Assuming a customer just ordered ane of these specialty coffees, determine the probabilities described below. a. What is the probability that the preparation time will be more than 39 seconds? b. What is the probability that the preparation time will be between 41 and 47 saconds? c. What percentage of these specialty coffees will be prepared within 49 seconds? d. What is the standard deviation of preparation times for this specialty coffee at this shop? a. Plpreparation time more than 39 seconds)- (Simplify your answer.) b. P(preparation time between 41 and 47 seconds) (Simplify your answer.) C. P(preparation time less than or equal to 49- (Simplifty your answer.) d. (Round to four decimal places as needed.) Enter your answer in each of the answer boxes.

Explanation / Answer

In a uniform distribution it is given that a=35 and b=55

a) P(X>39)=(55-39)/(55-35)=0.8

b) P(41<x<47)=(47-41)/(55-35)=0.3

c) P(x<49)=(49-35)/(55-35)=0.7

d) standard deviation is given by (b-a)/sqrt(12)=(55-35)/sqrt(12)=5.7735

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