Question

explain how you got your answers

in the united states 36% of the population has brown eyes. if 20 people are randomly selected find the probability that:

a) exactly 12 of them have brown eyes

b) less than 12 of them have brown eyes

c) at least 12 of them have brown eyes

Answer 1

Mean = np = 20 * 0.36 = 7.2

Standard deviation = sqrt (np(1-p) )

= sqrt (20 * 0.36 ( 1 - 0.36) )

= 2.1466

Using normal approximation,

P(X < x) = P(Z< X - Mean / SD)

a)

P(X = 12) = P(11.5 < X < 12.5) [ Using continuity correction. ]

= P(X< 12.5) - P(X < 11.5)

= P(Z < (12.5 - 7.2) / 2.1466) - P(Z < (11.5 - 7.2 ) / 2.1466)

= P(Z < 2.47) - P(Z < 2.00)

= 0.9932 - 0.9772

= 0.0160

b)

P(X < 12) = P(X < 11.5) [ Using continuity correction. ]

= P(Z < (11.5 - 7.2) / 2.1466)

= P(Z < 2.00)

= 0.9772

c)

P(X >= 12) = P(X > (11.5 - 7.2) / 2.1466) [ Using continuity correction. ]

= P(Z > 2.00)

= 0.0228