Question

In a recent study, 35% of people surveyed indicate chocolate was their favorite flavor of ice cream. Suppose we select a sample of 8 people and ask them to name their favorite flavor of ice cream.

How many of those in the sample would you expect to name chocolate? (Round your answer to 1 decimal place.)

What is the probability exactly four of those in the sample name chocolate? (Round the probability to 5 decimal places and the final answer to 4 decimal places.)

What is the probability four or more name chocolate? (Round your probability to 4 decimal places.)

Answer 1

Answer:-

Given That:-

35% of people surveyed indicate chocolate was their favorite flavor of ice cream. Suppose we select a sample of 8 people and ask them to name their favorite flavor of ice cream.

How many of those in the sample would you expect to name chocolate

Mean of a binomial probability distribution   

The probability exactly four of those in the sample name chocolate

Using the binomial probability formula

P(X) = ⁿC_r where n = 8 and  

Using the Combination Formula

ⁿC_r =

P(4) = ⁸C₄

=

= 40320/576 (0.01500) (0.17850)

= 70 (0.00267)

= 0.1869

The probability four or more name chocolate

First using the binomial probability formula

P(X) = ⁿC_r where n = 8 and  

Using the combination formula

ⁿC_r =

P(0) = ⁸C₀

=

= 8!/8! (1) (0.65)⁸

= (1)(1)(0.03186)

= 0.0319