A city police department plans to conduct a safety check point to check for vehi
ID: 3046306 • Letter: A
Question
A city police department plans to conduct a safety check point to check for vehicle occupants who are not wearing seat belts. Historically, it is known that 9% of vehicle occupants in this city do not wear their seat belts.
a. What is the probability that exactly one out of the first 12 vehicle occupants checked will not be wearing his/her seat belts?
Do not round intermediate calculations. Round your answer to four decimal places.
Probability =
b. What is the probability that exactly two out of the first 14 vehicle occupants checked will not be wearing his/her seat belts?
Do not round intermediate calculations. Round your answer to four decimal places.
Probability =
c. What is the probability that exactly three out of the first 16 vehicle occupants checked will not be wearing his/her seat belts?
Do not round intermediate calculations. Round your answer to four decimal places.
Probability =
Explanation / Answer
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
a.
P( X = 1 ) = ( 12 1 ) * ( 0.09^1) * ( 1 - 0.09 )^11
= 0.382718 ~ 0.3827
b.
P( X = 2 ) = ( 14 2 ) * ( 0.09^2) * ( 1 - 0.09 )^12
= 0.237697 ~ 0.2377
c.
P( X = 3 ) = ( 16 3 ) * ( 0.09^3) * ( 1 - 0.09 )^13
= 0.119799 ~ 0.1198
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