Question

Using the normal distribution, calculate the following probabilities:

1. a) P(X≤16|n=50, p=0.70)

2. b) P(10≤X≤16|n=50, p=0.50)

Answer 1

This is a binomial distribution question with
n = 50
p = 0.7
q = 1 - p = 0.3
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5
Since we know that

Type of this part: 1
a) x = 16
P(x < 16.0)=?

z = -5.8635
This implies that
P(x < 16.0) = P(z < -5.8635) = 0
b) This is a binomial distribution question with
n = 50
p = 0.5
q = 1 - p = 0.5
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5
Since we know that

x1 = 10
x2 = 16
P(10.0 < x < 16.0)=?

This implies that
P(10.0 < x < 16.0) = P(-4.2427 < z < -2.5456) = 0.0054