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Answer:
(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.
<em>Let </em><em> = sample proportion of households who own a 4K television.</em>
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
<em>Now, in the z table the P(Z </em><em> 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.</em>
Therefore, probability that in this sample of 150 households more than 50% own a 4K television is 0.00012.