Question

For a particular species of a flower, 50 percent have smooth leaves and 50 percent have hairy leaves. Suppose that you randomly pick 15 flowers of this species.

(a) Compute the expected number of flowers with smooth leaves.

μ=np=μ=np=  (Round to 2 decimal places.)

(b) Compute the probability that more than 8 flowers will have smooth leaves.

P(X>8)=1−P(X≤8)=P(X>8)=1−P(X≤8)=  (Round to 4 decimal places.)

(c) Compute the probability that exactly 5 flowers will have smooth leaves.

P(X=5)=P(X=5)=  (Round to 4 decimal places.)

Answer 1

a) n = 15

p = 0.5

µ = n * p = 15 * 0.5 = 7.5

b) P(X = x) = 15Cx * 0.5^x * 0.5^15-x

P(X > 8) = 1 - P(X < 8)

              = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8))

              = 1 - (15C0 * 0.5⁰ * 0.5¹⁵ + 15C1 * 0.5¹ * 0.5¹⁴ + 15C2 * 0.5² * 0.5¹³ + 15C3 * 0.5³ * 0.5¹² + 15C4 * 0.5⁴ * 0.5¹¹ + 15C5 * 0.5⁵ * 0.5¹⁰ + 15C6 * 0.5⁶ * 0.5⁹ + 15C7 * 0.5⁷ * 0.5⁸ + 15C8 * 0.5⁸ * 0.5⁷)

             = 1 - 0.6964

             = 0.3036

c) P(X = 5) = 15C5 * 0.5⁵ * 0.5¹⁰ = 0.0916