Question

Evidence suggests that 70% of FSU students like turtles. Suppose we randomly sampled 15 FSU students. Assume the binomial requirements are met. What is the probability 8 or fewer like turtles?

a.0.131

b.0.050

c.0.869

d.0.081

Answer 1

p = 0.7

n = 15

P(X = x) = 15Cx * 0.7^x * (1 - 0.7)^15-x

P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

              = 15C0 * 0.7⁰ * 0.3¹⁵ + 15C1 * 0.7¹ * 0.3¹⁴ + 15C2 * 0.7² * 0.3¹³ + 15C3 * 0.7³ * 0.3¹² + 15C4 * 0.7⁴ * 0.3¹¹ + 15C5 * 0.7⁵ * 0.3¹⁰ + 15C6 * 0.7⁶ * 0.3⁹ + 15C7 * 0.7⁷ * 0.3⁸ + 15C8 * 0.7⁸ * 0.3⁷

              = 0.1311

Option-A) 0.131