Suppose 53 percent of the population prefer red socks to gre

Suppose 53 percent of the population prefer red socks to green. If 100 random people are asked,

a. What is the probability that most (at least 50) will say prefer green (use the CLT) ?

Solution

Suppose 53 percent of the population prefer red socks to green. If 100 random people are asked,

a. What is the probability that most (at least 50) will say prefer green (use the CLT) ?

53 percent of the population prefer red socks to green

47 percent of the population prefer green

n=100

p=0.47

Expectation = np = 47

Variance = np(1 - p) = 24.91

Standard deviation = 4.991

P( x >=50) = P( z>(50-47)/4.991) = p( z > 0.60) = 0.2743

The required P= 0.2743