Homework SourseLocation LongTerm Mean of Clear Days in December Juneau Ala
Location Long-Term Mean % of Clear Days in December
Juneau, Alaska 18%
Seattle, Washington 24%
Hilo, Hawaii 36%
Honolulu, Hawaii 60%
Las Vegas, Nevada 75%
Phoenix, Arizona 77%
Estimate the probability that Juneau will have more than 7 clear days in December.
Estimate the probability that Seattle will have at most 4 clear days in December.
Estimate the probability that Seattle will have at most 10 clear days in December.
Estimate the probability that Seattle will have between 5 and 10 clear days in December.
Estimate the probability that Honolulu will have at least 16 clear days in December.
Estimate the probability that Las Vegas will have 20 or more clear days in December.
Estimate the probability that Phoenix will have from 20 to 25 clear days in December.
Solution
a) the probability that Juneau will have more than 7 clear days in December.
Here no of days = 31 =n
Success is x <=7. p = 0.18
As x is binomial
P(X<=7) = 0.8184
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the probability that Seattle will have at most 4 clear days in December.
= P(X<=4 for n =31: p = 0.24) = 0.1033
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the probability that Seattle will have at most 10 clear days in December
= P(X<=10 for n =31: p = 0.24) =0.8978
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the probability that Seattle will have between 5 and 10 clear days in December.
= P(10)-P(4) = 0.8978-0.1033
= 0.7945
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the probability that Honolulu will have at least 16 clear days in December.
= P(X>=16 for n =31: p = 0.6) = 0.8717
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the probability that Las Vegas will have 20 or more clear days in December.
= P(X>=20 for n =31: p = 0.75) = 0.9356
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the probability that Phoenix will have from 20 to 25 clear days in December.
= P(20<=X<=25 for n =31: p = 0.77) =P(x<=25) -P(X<=19) = 0.7498-0.0363
= 0.7135
