The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 5.5 minutes. (a) Calculate the expected arrival time. (Round your answer to 2 decimal place.) (b) What is the probability that an elevator arrives in less than 2.6 minutes

(a). 2.8 minutes.

(b). 0.4732

Explanation:

Without mincing words, let's dive straight into the solution to the question.

So, for the part (a), the expected arrival time can be calculated as given below.

The distribution falls between the ranges of 0(lower boundary) to 5.5minutes(upper boundary).

Therefore, the expected time = (0 + 5.5)÷ 2 = 2.75 minutes = 2.8 minutes(to 2 decimal places).

(b). The probability that an elevator arrives in less than 2.6 minutes can be calculated as given below;

Recall: We have that the upper boundary = 0 and the lower boundary = 5.5 minutes for the distribution. Also, the upper limit is equal to 2.6 minutes and the lower limits = 0 minutes.

Therefore, 1/ (5.5 - 0) = 1/5.5 = 0.182.

Therefore, the probability that an elevator arrives in less than 2.6 minutes = 0.182 ( 2.6 - 0).

The probability that an elevator arrives in less than 2.6 minutes = ( 0.182 × 2.6).

The probability that an elevator arrives in less than 2.6 minutes = 0.4732.