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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