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**

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