Question

The amount of time it takes for a student to complete a statistics quiz is uniormly distributed (or, given by a random variable that is uniformly distrbuted) between 27 and 55 minutes. One student la selected at random. Find the probability of the following ovents.

A The student requires more than 50 minutes to complote the quiz. Probabily = ________
B. The student completes the quiz in a time between 32 and 36 minutos. Probability = ________
C. The student completes the quiz in oxactly 43,74 minutes Probability = ________

Answer 1

To calculate the probability of different time events for a uniform distribution, we use the area under the curve between specified limits, with exact times having a probability of 0.

Step-by-step explanation:

The completion time for a statistics quiz is uniformly distributed between 27 and 55 minutes. To find the probability of certain events, we'll use the properties of a uniform distribution.

• A. To find the probability that a student requires more than 50 minutes to complete the quiz, we need to calculate the area under the distribution from 50 to 55, which can be done by the formula: P(X > a) = (b - a) / (b - a), where a is 50, b is 55, and a is 27.
• B. For a student to complete the quiz between 32 and 36 minutes, we again use the area under the curve formula P(a < X < b) = (b - a) / (b - a), where a is 32, b is 36.
• C. Since a uniform distribution is continuous, the probability of the student completing the quiz in exactly 43.74 minutes is 0.

These calculations allow us to find the desired probabilities.