(2 points) The amount of time it takes for a student to complete a statistics qu
ID: 3056063 • Letter: #
Question
(2 points) 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 34 and 59 minutes. One student is selected at random. Find the probability of the following events. A. The student requires more than 54 minutes to complete the quiz. Probability = B. The student completes the quiz in a time between 40 and 44 minutes. Probability = C. The student completes the quiz in exactly 43.26 minutes. Probability =Explanation / Answer
Solution:
Let X be the time it takes for a student to complete the quiz. We know that the PDF of X is:
f(x) = 1/59-34 = 1/25 , 34 x 59
a) We have to find the probability of the student requires more than 54 minutes completing the quiz.
P(X > 54) = (59 - 54) *1/25
= 5*1/25
= 1/5 = 0.2
Therefore, the probability that the X is greater than 54 is 0.2
b) We have to find the probability of the student completes the quiz in a time between 40 and 44 minutes.
P(40 < X < 44) = (44 - 40) * 1/25
= 6 *1/25 = 0.24
Therefore, the probability that the X lies between 40 and 44 is 0.24
c) We have to find the probability of the student completes the quiz in exactly 43.26
P(X = 43.26) = 0
Because there is an uncountable infinte number of a value of X, therefore the probability of each individual value is zero.
Threfore, the probability that the X is equals to 43.26 is 0.
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