Question

About 20% of Americans are bilingual. A random sample of 7 Americans is drawn. a) Find the probability that at most 3 are bilingual. b) Find the expected value and standard deviation.

Answer 1

solution

Given that ,

p = 0.20

1 - p = 1 - 0.20 = 0.80

n = 7

Using binomial probability formula ,

P(X = x) = (n C x) * px * (1 - p)n - x

P(X < 3 ) = P(X=0) +P(X=1)+P(X=2)+P(X=3)

= (7 C 0) * 0.200 * (0.80)7 +(7 C 1) * 0.201 * (0.80)6 +(7 C 2) * 0.202 * (0.80)5 +(7 C 3) * 0.203 * (0.80)5

probability =0.9667

(B)

expected value= = n * p = 7 * 0.20 = 1.4

expected value =   =1.4

Standard deviation = = n * p * q = 7 *0.20 *0.80 = 1.0583

Standard deviation = = 1.0583