Question

In the morning, about 25% of adults know what they will have for dinner. If one morning, you ask 22 adults if they know what they will have for dinner, what is the probability that more than 8 will say yes?

Group of answer choices

0.075

0.925

0.087

0.162

Answer 1

This is a binomial distribution

p = 0.25

n = 22

P(X = x) = ²²C_x * 0.25^x * (1 - 0.25)^22-x

P(X > 8) = 1 - (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))

              = 1 - (²²C₀ * 0.25⁰ * 0.75²² + ²²C₁ * 0.25¹ * 0.75²¹ + ²²C₂ * 0.25² * 0.75²⁰ + ²²C₃ * 0.25³ * 0.75¹⁹ + ²²C₄ * 0.25⁴ * 0.75¹⁸ + ²²C₅ * 0.25⁵ * 0.75¹⁷ + ²²C₆ * 0.25⁶ * 0.75¹⁶ + ²²C₇ * 0.25⁷ * 0.75¹⁵ + ²²C₈ * 0.25⁸ * 0.75¹⁴ )

              = 1 - 0.9254

              = 0.075

Option-A) 0.075