The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable

Question

2 months ago

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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 32 and 64 minutes. One student is selected at random. Find the probability of the following events.
A. The student requires more than 59 minutes to complete the quiz.
Probability =
B. The student completes the quiz in a time between 37 and 43 minutes.
Probability =
C. The student completes the quiz in exactly 44.74 minutes.
Probability =

Mathematics

1 answer:

Zina [12.3K] · Answer 1 · 2026-03-20T03:16:49+03:00

Answer:

(A) 0.15625

(B) 0.1875

(C) Cannot be determined

Step-by-step explanation:

The time it takes for a student to finish a statistics quiz is uniformly distributed between 32 and 64 minutes.

Let's denote X as the duration needed for the student to complete the statistics quiz

Thus, X ~ U(32, 64)

The probability density function (PDF) for a uniform distribution is expressed as;

f(X) = $\frac{1}{b-a}$ , a < X < b where a = 32 and b = 64

The cumulative distribution function (CDF) is given by P(X <= x) = $\frac{x-a}{b-a}$

(A) The probability of a student taking longer than 59 minutes to complete the quiz = P(X > 59)

P(X > 59) = 1 - P(X <= 59) = 1 - $\frac{x-a}{b-a}$ = 1 - $\frac{59-32}{64-32}$ = $1-\frac{27}{32}$ = 0.15625

(B) The probability that a student completes the quiz between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)

P(X <= 43) = $\frac{43-32}{64-32}$ = $\frac{11}{32}$ = 0.34375

P(X < 37) = $\frac{37-32}{64-32}$ = $\frac{5}{32}$ = 0.15625

P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875

(C) The probability that a student takes exactly 44.74 minutes to complete the quiz

= P(X = 44.74)

This probability cannot be calculated as it is a continuous distribution, which doesn't provide probabilities for specific points.