A brokerage survey reports that 31% of all individual investors have used a discount broker (one that does not charge the full commission). If a random sample of 120 individual investors is taken, approximate the probability that at least 39 have used a discount broker. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.) 0 X ? S

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### Normal Approximation to the Binomial Distribution

A brokerage survey reports that 31% of all individual investors have used a discount broker (one that does not charge the full commission). If a random sample of 120 individual investors is taken, approximate the probability that at least 39 have used a discount broker. Use the normal approximation to the binomial with a correction for continuity.

Round your answer to at least three decimal places. Do not round any intermediate steps.

(If necessary, consult a list of formulas.)

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**Explanation:**
This exercise involves approximating a binomial probability using a normal distribution. The binomial distribution counts the number of successes (in this case, using a discount broker) in a fixed number of trials (the 120 individual investors). Given the parameters, the normal distribution can serve as an approximation to the binomial distribution if the sample size is large enough, which is the case here. You will need to apply continuity correction because we are using a continuous distribution (normal) to approximate a discrete one (binomial).
Transcribed Image Text:### Normal Approximation to the Binomial Distribution A brokerage survey reports that 31% of all individual investors have used a discount broker (one that does not charge the full commission). If a random sample of 120 individual investors is taken, approximate the probability that at least 39 have used a discount broker. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.) _[Input Box]_ _[Check Button]_ _[Save For Later Button]_ _[Submit Answer Button]_ © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center --- **Explanation:** This exercise involves approximating a binomial probability using a normal distribution. The binomial distribution counts the number of successes (in this case, using a discount broker) in a fixed number of trials (the 120 individual investors). Given the parameters, the normal distribution can serve as an approximation to the binomial distribution if the sample size is large enough, which is the case here. You will need to apply continuity correction because we are using a continuous distribution (normal) to approximate a discrete one (binomial).
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