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In a large population, 46% of the households own DVD recorders. A simple random sample of 100 households is to be contacted and the sample proportion computed. The probability that more than half the households sampled will own a DVD recorder is:



Answer :

The probability that more than half the households sampled will own a DVD recorder is: 21.1%

How to find the p-value of proportions?

We are given;

Population proportion; p = 46% = 0.46

Sample size; n = 100

Sample proportion; p^ = 50% = 0.5

Now, the formula for z-score for proportions is;

z = (p^ - p)/√(p(1 - p)/n)

Plugging in the relevant values gives us;

z = (0.5 - 0.46)/√(0.46(1 - 0.46)/100)

z = (0.5 - 0.46)/√((0.46 * 0.54)/100)

z = 0.803

We want to find the probability that more than half the households sampled will own a DVD recorder. This is expressed as;

P(Z > 0.803) = 0.211 = 21.1%

Read more about p-value of proportions at; https://brainly.com/question/16828793

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