# According to a government study, 15% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:a) what is the probability that 5 or more live in poverty?b) what is the probability that 5 live in poverty?c) what is the expected number (mean) that live in poverty? What is the variance? What is the standard deviation?

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According to a government study, 15% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:
a) what is the probability that 5 or more live in poverty?
b) what is the probability that 5 live in poverty?
c) what is the expected number (mean) that live in poverty? What is the variance? What is the standard deviation?

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Step 1

The binomial distribution gives the probability of number of successes out of n trials in a series of Bernoulli trials.

The probability mass function (pmf) of a binomial random variable X is given as:

Let X is the number of children who live in poverty, which follows the binomial distribution.

It is given that the probability of a child who live in poverty is 0.15 and the sample size is 15.

Step 2

a).

The probability that 5 or more live in poverty is calculated as follows:

Now, the probability that X less than 5 can be calculated as follows.

The required probability is,

Therefore, the probability that 5 or more live in poverty is 0.064.

Step 3

b).

The probability that 5 live in poverty can be calculated as follows:

T...

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