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The weather in Rochester in December is fairly constant. Records indicate that the low temperature for each day
of the month tend to have a uniform distribution over the interval 15 to 35 F.
A business man arrives on a randomly selected day in December.
(a) What is the probability that the temperature will be above 17?
answer:
0.05
(b) What is the probability that the temperature will be between 19 and 32?
answer:
(c) What is the expected temperature?
answer:
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(a) The base interval for comparison is | 35 - 15 | = 20 degrees of F.
Working interval is | 35 - 17 | = 18 degrees of F.
The probability under the problem' question is the ratio of the working interval to the base interval
P = = = 0.9 = 90%. ANSWER. The answer 0.05 in your post is wrong.
(b) The base interval for comparison is | 35 - 15 | = 20 degrees of F.
Working interval is | 32 - 19 | = 13 degrees of F.
The probability under the problem' question is the ratio of the working interval to the base interval
P = = 0.65 = 65%. ANSWER.
(c) The expected value of the uniform distribution U(a,b) is the same as its mean .
Note, that this is precisely the midpoint of the interval [a,b] .
In this problem, the expected temperature is = = 25 degrees of F.
Solved.