The Aurora Borealis, otherwise known as the Northern Lights, is a natural light
ID: 3270308 • Letter: T
Question
The Aurora Borealis, otherwise known as the Northern Lights, is a natural light phenomenon that occurs in the sky, most often seen in the polar regions on the Earth. Suppose that there is a particular 7-day week in which there a 0.6 probability that the Aurora Borealis can be seen during any given day of this week. (a) What is the probability that the Aurora Borealis can be seen every day of this week? (b) What is the probability that the Aurora Borealis can be seen at least one day in this week? (c) What is the probability that the Aurora Borealis can be seen less than two days this week? (d) Find the mean, variance, and standard deviation for the number of days that the Aurora Borealis can be seen during this week.Explanation / Answer
a) P(X = 7)
Use excel function
BINOM.DIST(7,7,0.6,FALSE)
= 0.027994
b) P(X>=1)
= 1- P(X = 0)
=1-(0.4^7)
= 0.001638
c) P(x<2)
Use excel function
1-BNINOM.DIST(1,7,0.6,TRUE)
= 0.981158
d) Mean = 7*0.6 = 4.2
Variance = 7*0.6*0.4 = 1.68
Standard deviation = Sqrt(1.68) = 1.2961
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