The amount of time it takes for a student to complete a statistics quiz is unifo

Question

The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable that is uniformly distributed) between 35 and 64 minutes. One student is selected at random. Find the probability of the following events.

A. The student requires more than 58 minutes to complete the quiz.
Probability =

B. The student completes the quiz in a time between 39 and 44 minutes.
Probability =

C. The student completes the quiz in exactly 41.02 minutes.
Probability =

Explanation / Answer

For uniform distribution,

Lower cumulative = (x-a)/(b-a)

Upper Cumulative = (b-x)/(b-a)

Here, a = 35 minutes; b = 64 minutes

A.) x = 58 minutes

Since, we need to calculate the probability of X > 58.

We will use upper cumulative formula

P(X>58) = (64-58)/(64-35)

= 0.206

B.) P( 39 < x < 44) = (44-39)/(64-35)

= 0.1724

C.) x = 41.02

P( x=41.02) = 1/(64-35)

= 0.034

P( x = 41.02) =

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