The cable company takes an SRS (simple random sample) of 250 of the approximately 15,000 households who subscribe to them. They found that 75% of the sampled households watch sports on television at least once a month. The company is considering taking more samples like this. Suppose that it is actually 60% of their total subscribed households who watch those sports. Let p represent the proportion of a sample of 250 households that watch sports on television at least once a month. What are the mean and standard deviation of the sampling distribution of p?

Question

Aron Cooley

Mathematics

8 February, 15:41

The cable company takes an SRS (simple random sample) of 250 of the approximately 15,000 households who subscribe to them. They found that 75% of the sampled households watch sports on television at least once a month. The company is considering taking more samples like this. Suppose that it is actually 60% of their total subscribed households who watch those sports. Let p represent the proportion of a sample of 250 households that watch sports on television at least once a month. What are the mean and standard deviation of the sampling distribution of p?

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Sawyer Ingram · Answer 1

The mean of the sampling distribution of p is 0.75

The standard deviation of the sampling distribution of p is 0.0274

Step-by-step explanation:

According to the given data 75% of the sampled households watch sports on television at least once a month therefore the mean of the sampling distribution of p is 0.75.

In order to calculate the standard deviation of the sampling distribution of p we would have to use the following formula as follows:

Standard deviation = √ [ p (1 - p) / n ]

= √[ 0.75 * (1 - 0.75) / 250]

= 0.0274

The standard deviation of the sampling distribution of p is 0.0274.