Question

The life span of a certain insect in days is uniformly distributed over the interval (20,36). What is the probability the insect will live 24 days or less? Possible Answers a) .24 b) .25 c) .20 d) .75

Answer 1

Answer:

  b)  0.25

Step-by-step explanation:

The required probability is ...

  (24 -20)/(36 -20) = 4/16 = 1/4 = 0.25

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Comment on the attached graph

The red line is the probability distribution function (pdf) for this uniform distribution. The green line is the cumulative distribution function (cdf) for this uniform distribution. It is the integral of the pdf.

The probability of interest is the value of the cdf at x=24. That value is 0.25, meaning the area under the pdf curve to the left of x=24 is 1/4 of the total area under the pdf curve. That proportion is what is calculated above.