High temperatures in a certain city for the month of August follow a uniform distribution oveer the interval 61 degrees F and 85 degrees F. What is the probability that a randomly selected August day has a high temperature that exceeded 66 degrees F? Show your work.
a) 0.452, 1
b) 0.791, 7
c) 0.208, 3
d) 0.041, 7
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The probability for a uniform distribution is calculated by the formula:
P(a ≤ X ≤ b) = (b - a) / (n - m)
where:
- X is the random variable (in this case, the high temperature)
- a and b are the bounds of the event we're interested in (in this case, 66 and 85 degrees)
- m and n are the bounds of the entire distribution (in this case, 61 and 85 degrees)
So, the probability that the high temperature exceeds 66 degrees is:
P(66 ≤ X ≤ 85) = (85 - 66) / (85 - 61) = 19 / 24 = 0.791, 7
So, the correct answer is (b) 0.791, 7.
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