Question

​n=150

N10000

p=.4

(b) What is the probability of obtaining x=63 or more individuals with the​ characteristic? That​ is, what is ​P(^p greater or equal to 0.42​)?

(c) What is the probability of obtaining x=54 or fewer individuals with the​ characteristic? That​ is, what is ​P(^p less than or equal to 0.36)?

Answer 1

xN(np, np(1 p)) X ~N(60,36)

We need to calculate:

b)

P(X 63)

Using continuity correction:

P(X 63)- P(X > 62.5)

The following information has been provided: We need to compute PrX 62.5). The corresponding z-value needed to be computed is X μ 62.5.60 Therefore, we get that z62.5-60Pr(z0.4167) Pr(X > 62.5) = Pr (Z > 02.6 = 1-0.6615 0.3385

c)

P(X < 54)P(X < 54.5)

The following information has been provided: μ=60, σ = 6 We need to compute Pr(X54.5). The corresponding z-value needed to be computed: X μ-54.5 60 = 0.9167 Therefore Pr(Z <-0.9167) 0.1797