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The maximum temperature reached on any day can be classified as above freezing (a success) or below freezing (a
failure). In a certain city of eastern North America, January weather statistics indicate the probability a January day
will be above freezing is 0.3. Use the binomial distribution to determine the following probabilities:
a. Exactly 2 of the next 7 January days will be above freezing.
b. More than 5 of the next 7 days will be above freezing.
c. There will be at least 1 day above freezing in the next 7 days.
d. All 7 days in the next week will be above freezing.
e. Is this a reasonable application of the binomial distribution? Why or why not?
SOLUTION:
a. Exactly 2 of the next 7 January days will be above freezing.
Using binomial distribution,
n=7and
,3.0=
.3177.0)7.0()3.0)(2,7()2(
52
== CP
b. More than 5 of the next 7 days will be above freezing.
.0288.00002.00036.00250.0)7()6()5( =++=++ PPP
c. There will be at least 1 day above freezing in the next seven days
.9176.00824.01)0(1 == P
d. All 7 days in the next week will be above freezing.
0002.0)7( =P
.
e. Is this a reasonable application of the Binomial distribution? Why or why not?
No, because weather changes is independent. We cannot apply binomial distribution
due to this reason. Weather is successive and independent.
THANK YOU

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The maximum temperature reached on any day can be classified as above freezing (a success) or below freezing (a failure). In a certain city of eastern North America, January weather statistics indicate the probability a January day will be above freezing is 0.3. Use the binomial distribution to determine the following probabilities: a. Exactly 2 of the next 7 January days will be above freezing. b. More than 5 of the next 7 days will be above freezing. c. There will be at least 1 day above freezing in the next 7 days. d. All 7 days in the next week will be above freezing. e. Is this a reasonable application of the binomial distribution? Why or why not? SOLUTION: a. Exactly 2 of the next 7 January days will be above freezing. Using binomial distribution, n=7and  = 0.3, P(2) = C (7,2)(0.3) 2 (0.7) 5 = 0.3177. b. More than 5 of the next 7 days will be above freezing. P(5) + P(6) + P(7) = 0.0250 + 0.0036 + 0.0002 = 0.0288. c. There will be at least 1 day above freezing in the next seven days 1 − P(0) = 1 − 0.0824 = 0.9176. d. All 7 days in the next week will be above freezing. P(7) = 0.0002 . e. Is this a reasonable application of the Binomial distribution? Why or why not? No, because weather changes is independent. We cannot apply binomial distribution due to this reason. Weather is successive and independent. THANK YOU Name: Description: ...
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