SOLUTION: Of all new vehicles of a certain model that are sold, 20% require repairs to be done under warranty during the first year of service. A particular dealership sells 12 such vehicles

Question 1188777: Of all new vehicles of a certain model that are sold, 20% require repairs to be done under warranty during the first year of service. A particular dealership sells 12 such vehicles.
(a)
Determine the probability that exactly four of them require warranty repairs.
(b)
Determine the probability that less than three of the vehicles require warranty repairs,
(c)
Determine the standard deviation of the vehicles that require warranty repairs.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the expected value is np or 12*0.2=2.4 of them require repairs
the variance is 2.4*0.8= (np(1-p)=1.92
sd is sqrt (V)=1.386
-
exactly 4 is 12C4*0.2^4*0.8^8=0.1329
binompdf(12,0.2,4)=0.1329
-
fewer than 3 is 0,1,2
for 0 it is 0.8^12=0.0687
for 1 it is 12*0.2*0.8^11=0.2062
for 2 it is 12C2*0.2^2*0.8^10=0.2835
that sum is 0.5584
may confirm by binomcdf(12,0.2,2)ENTER=0.5583 (so slight rounding error)
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