# In a recent study 35 % of people surveyed indicate chocolate was their favourite flavor ice...

## Question:

In a recent study {eq}35 \ \% {/eq} of people surveyed indicate chocolate was their favourite flavor ice cream. Suppose we select a sample of ten and ask them to name their favourite flavor of ice cream.

(a) How many would you expect to name chocolate?

(b) What is the probability exactly four of those in the sample name chocolate?

(c) What is the probability four or more is named chocolate?

## Binomial Probability Distribution:

Binomial distribution is a type of discrete probability distribution that gives sequence of successes repeated in a given number of Bernoulli trials. The probability of success remains constant throughout the experiment.

## Answer and Explanation:

**a).**

Given that;

{eq}n=10\\p=0.35 {/eq}

The expected number of binomial distribution is equal to the mean:

{eq}\begin{align*} E(x)&=\mu=np\\&=10\times 0.35\\&=3.5 \end{align*} {/eq}

**b).**

Use binomial probability mass function to calculate the probability of exactly four people who will indicate that chocolate is their favour color ice cream:

{eq}\begin{align*} b(n,x,p)&=^nC_xp^x(1-p)^{n-x}\\b(10,4,0.35)&=^{10}C_{4}\cdot 0.35^4(1-0.35)^{10-4}\\&=210\times 0.35^4\times 0.65^6\\&=0.2377 \end{align*} {/eq}

**c).**

Use binomial probability calculator to find the probability of getting more than four:

{eq}\begin{align*} P(X\ge 4)&=P(X=4)+P(X=5)...+P(X=10)\\&=0.4862 \end{align*} {/eq}

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