Question

The incidence of major depression in adults is about 10%. A random sample of 50 adults will be tested for depression. The variable X is the number of individuals diagnosed with depression among all 50 and has the binomial distribution Bin(n = 50, p = 0.1). The probability that exactly 2 adults in the sample have depression is A) 0.010 B) 0.020 C) 0.078 D) 0.100 E) 0.112

Answer 1

Given:

X ~ Bin(50,0.1)

P.M.F of X

n P(X = 1) = p" (1 – p)-2

where, n=50 and p=0.1

P(X = 2) = (29)0.1°(1 – 0.13-2

50 *0.12 * 0.94 2

=1225 * 0.12*0.98 = 0.07790.078

The probability that excatly 2 adults in the sample have depression is

C) 0.078

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