In each sample of water taken from homes in Flint has 12% chance of having high
ID: 3180349 • Letter: I
Question
In each sample of water taken from homes in Flint has 12% chance of having high levels of lead in their supply water's pipes. 35 homes were selected in Flint Michigan and water samples were taken from their supply water pipes to find out if they have high levels of lead in them. Assume these homes selected are independent with regards of having high levels of lead in their supply water's pipes. A) Calculate the mean mu x for this distribution. B) Calculate the standard deviation sigma x for is distribution. C) Calculate the probability that exactly 3 homes will have high levels of lead in their supply water's pipes. D) Calculate the probability that less than 4 homes will have high levels of lead in their supply water's pipes.Explanation / Answer
a.
Mean ( np ) =35 * 0.12 = 4.2
b.
Standard Deviation ( npq )= 35*0.12*0.88 = 1.9225
c.
Binomial 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
P( X = 3 ) = ( 35 3 ) * ( 0.12^3) * ( 1 - 0.12 )^32
= 0.1892
d.
P( X < 4) = P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 35 3 ) * 0.12^3 * ( 1- 0.12 ) ^32 + ( 35 2 ) * 0.12^2 * ( 1- 0.12 ) ^33 + ( 35 1 ) * 0.12^1 * ( 1- 0.12 ) ^34 + ( 35 0 ) * 0.12^0 * ( 1- 0.12 ) ^35
= 0.3811