Question

n a recent survey, 40% indicated chocolate was their favorite flavour of ice cream. Suppose that we select a sample of 14 people and ask them to name their favourite flavour of ice cream.

a. How many of those in the sample would you expect to name chocolate? (Round the final answer to 2 decimal place.)

Probability ___________

b. What is the probability exactly eight of those in the sample name chocolate? (Do not round the intermediate values. Round the final answer to 4 decimal places.)

Probability ___________

c. What is the probability eight or more name chocolate? (Do not round the intermediate values. Round the final answer to 4 decimal places.)

Probability ______________

Answer 1

X ~ Binomial (n,p)

Where n = 14 , p = 0.40

P(X) = ⁿC_x p^x (1 - p)^n-x

a)

E(X) = np

= 14 * 0.40

= 5.6

b)

P( X = 8) = ¹⁴C₈ 0.40⁸ 0.60⁶

= 0.0918

c)

P( X >= 8) = P( X = 8) + P( X = 9) + P( X = 10) + P( X = 11) + P( X = 12) + P( X = 13) + P( X = 14)

= ¹⁴C₈ 0.40⁸ 0.60⁶ +¹⁴C₉ 0.40⁹ 0.60⁵ +¹⁴C₁₀ 0.40¹⁰ 0.60⁴ +¹⁴C₁₁ 0.40¹¹ 0.60³ +¹⁴C₁₂ 0.40¹² 0.60²

+¹⁴C₁₃ 0.40¹³ 0.60¹ +¹⁴C₁₄ 0.40¹⁴ 0.60⁰

= 0.1501