Question

According to the 2016 study by the Pew research 74 percent of adults American have read at least one book in the past 12 months a sample of 10 adult americans is randomly selected le t x be the randem variable representing the number of people who have read at least on book explain why x is a binomial random variable by filling the blanks below in this problem a trial is------------- the number of trials n=--------------

Answer 1

x is a binomial random variable because a trial is independent and number of trials, n = 10.

Explanation:

We are given the following information:

We treat adult reading at least one book in the past 12 months as a success.

P(Adult reading atleast one book) = 74% = 0.74

Then the number of adults follows a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

If x is a random variable representing the number of people who have read at least on book, then x follows a binomial distribution because:

• There are n independent trials. Here, n = 10.
• Each trial have two possible outcome either a success(read atleast one book) or a failure(not read atleast one book)
• The probability of success is same for each trial. Here p = 0.74

Thus,

x is a binomial random variable because a trial is independent and number of trials, n = 10.