For the normal approximation to the binomial distribution with n = 100 and p = 1/5,the probability of selecting a score greater than or equal to 25 is p = 0.1056.

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Quizplus · Accepted Answer

The normal approximation to the binomial distribution requires calculating the mean (μ) and standard deviation (σ) of the binomial distribution, then using these to find the z-score for the value of interest (in this case, 25), and finally using the z-score to find the probability. The mean μ = np = 100 * (1/5) = 20, and the standard deviation σ = sqrt(np(1-p)) = sqrt(100 * (1/5) * (4/5)) = sqrt(16) = 4. To find the probability of selecting a score greater than or equal to 25, one would calculate the z-score for 24.5 (for continuity correction) and then find the corresponding probability from the standard normal distribution. The exact probability value of 0.1056 does not directly follow from this process without performing the actual calculations and using standard normal distribution tables or software.

For the Normal Approximation to the Binomial Distribution with N