The time required to prepare a certain specialty coffee at a local coffee shop i
ID: 3048450 • Letter: T
Question
The time required to prepare a certain specialty coffee at a local coffee shop is uniformly distributed between 20 and 60 seconds. Assuming a customer just ordered one of these specialty coffees, determine the probabilities described below. a. What is the probability that the preparation time will be more than 23 seconds? b. What is the probability that the preparation time will be between 32 and 49 seconds? c. What percentage of these specialty coffees wil be prepared within 47 seconds? d. What is the standard deviation of preparation times for this speciality coffee at this shop? a. P(preparation time more than 23 seconds) (Simplity your answer.)Explanation / Answer
a) probability that preparation time more than 23 seconds.
The provided lower limit of the distribution is a=20, and the upper limit is b=60. We need to compute Pr(X >23)
Therefore, the following is obtained:
Pr(X > 23) = { 60 - 23 }/{ 60 - 20} = 0.925
b) The Probability that the preparation time will be between 32 and 49 seconds.
The provided lower limit of the distribution is a=20, and the upper limit is b=60. We need to compute Pr(32X49)
Therefore, the following is obtained:
Pr(32X49)=6020/ 4932=0.425
c) Probability that less than 47 seconds
The provided lower limit of the distribution is a=20, and the upper limit is b=60. We need to compute Pr(X47)
Therefore, the following is obtained:
Pr(X47)=6020/4720=0.675
d) Variance of uniform distribution is
(b-a)^2/12 = ( 60-20)^2/12= 1600/12= 133.33
Std = sqrt(133.33)= 11.55
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