Question

Nationwide tests indicate that about 30% of 12-year-olds can identify the state of Colorado on a map of the United States. Suppose we select a random sample of 20 12-year-olds, and ask them to identify the state of Colorado on a map of the United States. Please show all work

What is the probability that at most 8 of them will be successful?

Answer 1

Solution :

Given that,

p = 30% = 0.30

q = 1 - p = 1 - 0.30 = 0.70

n = 20

Using binomial distribution,

= n * p = 20 * 0.30 = 6

= n * p * q = 20 * 0.30 * 0.70 = 2.0494

Using continuity correction ,

P(x 8.5) = P((x - ) / (8.5 - 6) / 2.0494)

= P(z 1.194)

= 0.8838   

Probability = 0.8838