In the United States, 35% of households own a 4K television. Suppose we take a random sample of 150 households. (a) Describe the distribution of the sample proportion. (b) What is the probability that in this sample of 150 households that more than 50% own a 4K television

(a) The distribution of the sample proportion is Normal distribution.

(b) The probability that in this sample of 150 households that more than 50% own a 4K television is 0.00012.

Step-by-step explanation:

We are given that in the United States, 35% of households own a 4K television.

Suppose we take a random sample of 150 households.

Let = sample proportion of households who own a 4K television.

The z-score probability distribution for sample proportion is given by;

           Z =  ~ N(0,1)

where, = sample proportion

     p = population proportion of households own a 4K television = 35%

     n = sample of households = 150

(a) The distribution of the sample proportion is related to the Normal distribution.

(b) Probability that in this sample of 150 households more than 50% own a 4K television is given by = P( > 0.50)

    P( > 0.50) = P( > ) = P(Z > 3.67) = 1 - P(Z 3.67)

                                                                   = 1 - 0.99988 = 0.00012

Now, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.67 in the z table which has an area of 0.99988.

Therefore, probability that in this sample of 150 households more than 50% own a 4K television is 0.00012.

a - base

b - exponent

so,