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

Answer 1

Complete 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 6 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:

a

The possible value of x is 0, 1 ,2,3,4,5,6,7,8,9,10

b

$P(X = 6) = 0.158$

Step-by-step explanation:

From the question we are told that

 The proportion that stated that they have not purchased organic fruits or vegetables is $p =0.74$

   The sample size is  n = 10

The possible value x can take is  0, 1 ,2,3,4,5,6,7,8,9,10

Generally the probability that exactly 6  households in a random sample of 10 will say that they have never purchased organic fruits or vegetables is mathematically represented as

      $P(X = 6) = ^nC_6 * p^{6}* (1-p)^{n-6}$

Here C denotes combination

So

        $P(X = 6) = ^{10}6 * (0.74)^{6}* (1-0.74)^{10-6}$

=>    $P(X = 6) = 0.158$