According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses a SRS of 300 children. Estimate the probability that between 60 and 63 children of the sample are from poverty households?

The estimated probability that between 60 and 63 children of the sample are from poverty households is 0.1367.

Step-by-step explanation:

Let X = number of American children under the age of 6 live in households with incomes less than the official poverty level.

The probability of the random variable X occurring is, p = 0.22.

A random sample of children of size n = 300 is selected.

The random variable X follows a Binomial distribution with parameters n = 300 and p = 0.22.

A normal approximation to Binomial can be used to approximate the distribution of X if the following conditions are fulfilled:

Check:

So, the random variable X approximately follows N (np, np(1 - p)).

Compute the probability of X between 60 and 63 as follows:

*Use a z-table for the probability values.

Thus, the estimated probability that between 60 and 63 children of the sample are from poverty households is 0.1367.

( 8x - 8)^3/2 = 64

√(8x - 8)^3 = 64

(8x - 8)^3 = 4096

8x - 8 = 16

8x = 16 + 8

8x = 24

X= 3

So, the answer is X= 3