Answer to Question #191389 in Statistics and Probability for Gio Fuentes

Question

A local paper claims the proportion of college students who own a car is 38%. In a sample of 275 college students, what is the probability that more than 116 will own a car?

Answer 1

$p = 0.38 \\ q = 0.62 \\ n = 275$

Using binomial distribution:

Mean:

$\mu = n \times p = 275 \times 0.38 = 104.5$

Standard deviation:

$\sigma = \sqrt{n \times p \times q} = \sqrt{275 \times 0.38 \times 0.62} = 8.05 \\ P(X>116) = 1 -P(X<116) \\ = 1 -P(Z< \frac{116-104.5}{8.05}) \\ = 1 -P(Z<1.428) \\ = 1 -0.9233 \\ = 0.0767$