Probability and standard deviation questions need some help A recent study by the American Highway Patrolman’s Association revealed that 65% of American drivers use their seatbelts. A sample of 12 drivers on major highways was randomly selected. a. Find the probability that seven of the drivers are wearing seatbelts. b. How many of the drivers would be expected to be wearing their seatbelt? c. Calculate the standard deviation for this distribution

Background:

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In _Mathematica_ :


N@Binomial[12, 7] (.65^7 (1 - .65)^(12-7)


a) ${12 \choose 7} .65^7 (1-.65)^{12-7} = .2039$


Mean[BinomialDistribution[12, .65]]


b) $ .65 \times 12 = 7.8$


Variance[BinomialDistribution[12, .65]]


c) $Var = n p (1-p) = 12 \times 0.65 (1 - 0.65) = 2.73$