Q:

Suppose the probability of producing a defective light bulb from a production line is the same over an interval of 90 minutes. Which of the following distributions would you use to determine the probability that a defective light bulb will be produced in a 15-minute interval? A) Normal distribution B) Poisson distribution C) Uniform distribution D) Exponential distribution

Accepted Solution

A:
Answer:C) Uniform distributionStep-by-step explanation:An uniform probability is a case of probability in which each outcome is equally as likely. In this case, the probability of producing a defective light bulb from a production line is the same over an interval of 90 minutes, so the correct answer is C.We can calculate the probability.Uniform probability distributionFor this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.The probability that we find a value X lower than x is given by the following formula.[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]For this problem, we have that:Uniformily distributed over a 90 minute interval, that is, between 0 and 90, so [tex]b = 90[/tex] and [tex]a = 0[/tex].We want to find [tex]P(X \leq 15) = \frac{15-0}{90-0} = 0.167[/tex]