Question

Problem 1: 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? (Hint: It should be a very small probability)

Answer 1

Solution

Given that,

p = 0.35

1 - p = 1 - 0.35 = 0.65

n = 150

a) = p = 0.35

=  [p( 1 - p ) / n] = [(0.35 * 0.65) / 150 ] = 0.0389

b) P( > 0.50) = 1 - P( < 0.50 )

= 1 - P(( - ) / < (0.50 - 0.35) / 0.0389)

= 1 - P(z < 3.86)

Using z table

= 1 - 0.9999

= 0.0001