Question

It has been reported that 72% of Americans favor FBI background checks for people who purchase guns at gun shows. A random sample of 8 people is chosen. Calculate the probability that 5 people in this sample favor background checks. Use Binomial formula

Answer 1

Solution

Given that ,

p = 72% = 0.72

1 - p = 1 - 0.72 = 0.28

n = 8

x = 5

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X = 5) = ((8! / 5! (8 - 5)!) * 0.72⁵ * (0.28)^{8 - 5}

=  ((8! / 5! (3)!) * 0.72⁵ * (0.28)³

= 0.2379

Probability = 0.2379