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According to a recent ratings report, 15.4% of households watch a certain television series on a regular basis. Estimate the probability that fewer than 70 in a random sample of 500 households are watching the series on a regular basis.

User Stromgren
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Answer: To estimate the probability that fewer than 70 households in a random sample of 500 are watching the series on a regular basis, we can use the binomial probability formula:

P(X < 70) = Σ [nCx * p^x * (1 - p)^(n - x)]

where:

P(X < 70) = Probability that X is less than 70

n = Total number of trials (in this case, the sample size = 500 households)

x = Number of successes we want to find the probability for (in this case, the number of households watching the series)

p = Probability of success in a single trial (in this case, 15.4% = 0.154)

(1 - p) = Probability of failure in a single trial (1 - 0.154 = 0.846)

Now, let's calculate the probability:

P(X < 70) = Σ [500C0 * (0.154)^0 * (0.846)^500 + 500C1 * (0.154)^1 * (0.846)^499 + 500C2 * (0.154)^2 * (0.846)^498 + ... + 500C69 * (0.154)^69 * (0.846)^431]

Since calculating the summation manually can be time-consuming, we can use statistical software or a calculator with the binomial cumulative probability function to find the result directly. For example, in Python, you can use the scipy library:

n = 500

p = 0.154

x = 69

The output will give you the estimated probability that fewer than 70 households in a random sample of 500 are watching the series on a regular basis.

User Eweb
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