Answer to Question #273325 in Statistics and Probability for Nis

Question

The amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability following events

Answer 1

The amounts of time it takes for a student to complete a statistics quiz uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events.

a) the student requires more than 55 minutes to complete quiz

b) the student completes the quiz in a time between 30 and 40 minutes

c) the student completes the quiz in exactly 37.23 minutes

It is given that the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 30 and 60 minutes.

The probability density function for the random variable is obtained below.

$f(x) = \frac{1}{b-a}; a<x<b \\ = \frac{1}{60-30} \\ = \frac{1}{3}, 30 ≤x≤60$

(a) We have to find the probability of the student requires more than 55 minutes completing the quiz.

$P(X>55) = (60-55) \times \frac{1}{30} \\ = 5 \times \frac{1}{30} \\ = \frac{1}{6} \\ = 0.1667$

Therefore, the probability that the X is greater than 55 is 0.1667.

(b) We have to find the probability of the student completes the quiz in a time between 30 and 40 minutes.

$P(30<X<40) = (40-30) \times \frac{1}{30} \\ = 10 \times \frac{1}{30} \\ = \frac{1}{3} \\ = 0.3333$

Therefore, the probability that the X lies between 30 and 40 is 0.3333.

(c) We have to find the probability of the student completes the quiz in exactly 37.23 minutes.

P(X=37.23) =0

Because there is an uncountable infinite number of a value of X, therefore the probability of each individual value is zero.

Therefore, the probability that the X is equals to 37.23 is 0.