Question

In a recent survey, 37% indicated chocolate was their favorite flavour of ice cream. Suppose that we select a sample of 12 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 six 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 six or more name chocolate? (Do not round the intermediate values. Round the final answer to 4 decimal places.)

Probability         

Answer 1

This is a direct application of binomial distribution.

Let X be a number of people whose favorite flavour of ice cream is chocolate.

X ~ Binomial ( n = 12, p = 0.37)

a) Number of people expect to name chocolate is,

np = 12 * 0.37 = 4.44

=> Answer: 4.44

Using Excel we find, the following binomial probabilities,

b) P(X = 6) = BINOMDIST(6, 12, 0.37, 0) = 0.1482

=> Probability = 0.1482

c)

P(X >= 6)

= 1 - P(X < 6)

= 1 - P(X <= 5)

= 1 - BINOMDIST(5, 12, 0.37, 1)

= 0.2587

=> Probability = 0.2587