Please write a detailed solution for each of the following problems and upload y
ID: 3365558 • Letter: P
Question
Please write a detailed solution for each of the following problems and upload your work to Taskstream in a PDF format via eCourse Note: Computation Skills) Suppose a study is conducted using adults in a particular county. They found that 52% of the adults in the county are males. In addition to the above, they found that 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars. If an adult is chosen randomly, what is the probability that an adult is a male given that selected adult smokes cigars? 2. (Computation Skills) Automobiles arrive at a vehicle equipment inspection station according to a Poisson process with a rate of 10 per hour. What is the probability that there are at most 6 vehicles coming to the inspection during an hour? a. an hour? What is the probability that there are exactly 6 vehicles coming to the inspection during an hour? c.Explanation / Answer
Q2.
POSSION DISTRIBUTION
pmf of P.D is = f ( k ) = e- x / x!
where
= parameter of the distribution.
x = is the number of independent trials
I.
mean =
= 10
a.
P( X < = 6) = P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= e^-10 * 10 ^ 6 / 6! + e^-10 * 0 ^ 5 / 5! + e^-10 * ^ 4 / 4! + e^-10 * ^ 3 / 3! + e^-10 * ^ 2 / 2! + e^-10 * ^ 1 / 1! + e^-10 * ^ 0 / 0!
= 0.13014,
P( X > 6) = 1 -P ( X <= 6) = 1 - 0.1301 = 0.86986
b.
P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= e^-10 * 0 ^ 5 / 5! + e^-10 * ^ 4 / 4! + e^-10 * ^ 3 / 3! + e^-10 * ^ 2 / 2! + e^-10 * ^ 1 / 1! + e^-10 * ^ 0 / 0!
= 0.06709
P( X > = 6 ) = 1 - P (X < 6) = 0.93291
c.
P( X = 6 ) = e ^-10 * 10^6 / 6! = 0.06306