Let X be a binomial random variable (n=22, p=0.7) representing the number of pat
ID: 3259770 • Letter: L
Question
Let X be a binomial random variable (n=22, p=0.7) representing the number of patients who had been screened in the previous three years, among a group of 20 patients visiting a health clinic on a certain day. (There are 20 patients visiting the clinic this day, and this clinic is in a city that has a screening program that has reached 70% of the population within the last 3 years.) a. Find P(X = 14 or 15). b. Find the expected value mu = E(X), sigma^2 = Var(x), and sigma. Suppose A and B are two events such that P(A) = 0.65, P(B) = 0.5, and P(A and B) = C.2 a. Find P(A or B). b. Find P(not A). c. Find P(not B)Explanation / Answer
Answer:
13).
a).
n=20, p=0.7
P(X=x) = (nCx) px (1-p)n-x
P( x=14 or 15) = P( x=14)+P( x=15)
= 0.1916+ 0.1789
=0.3705
b).
Expectation = np = 14
Variance = np(1 - p) = 4.2
Standard deviation = 2.0494
14). P( A) =0.55 P( B) =0.5 P( A and B) =0.2
a). P( A or B) = P( A)+P( B)-P( A and B)
=0.65+0.5-0.2
=0.95
b). P( not A) = 1-P( A) = 1-0.65
=0.35
c).
P( not B) = 1-0.5
=0.5
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