3. In the Southwest, 5% of all cell phone calls are dropped. a. What is the prob
ID: 3066978 • Letter: 3
Question
3. In the Southwest, 5% of all cell phone calls are dropped. a. What is the probability that out of six randomly selected calls, none was dropped? Exactly one? Exactly two? Exactly three? Exactly four? Exactly five? Exactly six out of six? b. What is the probability that at least 4 calls are dropped? c. What is the probability that less than 4 calls are dropped? d. What is the probability that at least 1 but at most 3 calls out of 6 are dropped? e. What is the average number of calls out of six that will be dropped? f. What is the variance of the number of calls out of six that will be dropped?Explanation / Answer
a) P(X = 0)
Use Excel function
BINOM.DIST(0,6,0.05,FALSE)
= 0.7351
P(X = 1)
Use Excel function
BINOM.DIST(1,6,0.05,FALSE)
= 0.2321
P(X = 2)
Use Excel function
BINOM.DIST(2,6,0.05,FALSE)
= 0.0305
P(X = 3)
Use Excel function
BINOM.DIST(0,6,0.05,FALSE)
= 0.0021
P(X = 4)
Use Excel function
BINOM.DIST(4,6,0.05,FALSE)
= 0.0001
P(X = 5)
Use Excel function
BINOM.DIST(5,6,0.05,FALSE)
= 0.0000
P(X = 6)
Use Excel function
BINOM.DIST(6,6,0.05,FALSE)
= 0.0000
b) P(X>=4)
P(X = 0)
Use Excel function
1-BINOM.DIST(3,6,0.05,TRUE)
= 0.0001
c) P(X <4)
Use Excel function
BINOM.DIST(3,6,0.05,TRUE)
= 0.9999
d) P(1<=X<=3)
Use Excel function
BINOM.DIST(3,6,0.05,TRUE)-BINOM.DIST(0,6,0.05,TRUE)
= 0.2648
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