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November 10th, 2017, 01:27 PM   #1
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Continuous Uniform Distribution

I need help figuring out whether I did the following problem correctly.

You were informed at the nursery that your peach tree will definitely bloom sometime between March 18 and March 30. Assume that the bloom times follow a Continuous Uniform Distribution between these dates.

A. What is the probability that the tree does not bloom until March 25?

I translated that as P(X>25) = (30-25)*1/30 - 18 and I got 0.417 as my answer.

B. What is the probability that the tree will bloom by March 20?

I translated that as P(X<20) = (20-18)*1/30 - 18 and I got 0.167 as my answer.

Last edited by skipjack; November 10th, 2017 at 07:15 PM.
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November 11th, 2017, 12:36 PM   #2
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$f_B(t) = \dfrac{1}{30-18} = \dfrac{1}{12},~t \in [18,30]$

$F_B(t) = \dfrac{t-18}{12},~t \in [18,30]$

$P[t\geq 25]=1-F_B(25)=1-\dfrac{25-18}{12} = 1-\dfrac{7}{12}=\dfrac{5}{12}\approx 0.4167$

$P[t\leq 20] = F_B(20)=\dfrac{20-18}{12} = \dfrac{1}{6}\approx 0.1667$

so it looks like you got it right, even if you did it in a bit of an unusual way.
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