Question

According to a survey, 74% of households said that they have never purchased organic fruits or vegetables. Suppose that this result is true for the current population of households.

a. Let x be a binomial random variable that denotes the number of households in a random sample of 10 who have never purchased organic fruits or vegetables. What are the possible values that x can assume?
Integers to ______.
b. Find to 3 decimal places the probability that exactly 7 households in a random sample of 10 will say that they have never purchased organic fruits or vegetables. Use the binomial probability distribution formula.
Probability = ______.

Answer 1

(a) S = {0, 1, 2, ..., 10}

(b) 0.256

Explanation:

It is provided that, 74% of households said that they have never purchased organic fruits or vegetables.

(a)

X = the number of households in a random sample of 10 who have never purchased organic fruits or vegetables.

X follows a binomial distribution.

The sample space of X is:

S = {0, 1, 2, ..., 10}

(b)

Compute the probability that exactly 7 households in a random sample of 10 will say that they have never purchased organic fruits or vegetables as follows:

`P(X=7)={10\choose 7}(0.74)^(7)(1-0.74)^(10-7)`

`=120* 0.121513* 0.017576\\\\=0.25628549856\\\\\approx 0.256`

Thus, the probability that exactly 7 households in a random sample of 10 will say that they have never purchased organic fruits or vegetables is 0.256.