In Exercises 9–14, write the binomial probability in words. Th...

Question

In Exercises 9–14, write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability.

P(55 < x < 60)

Accepted Answer

Hello everyone. Let's take a look at this question together. A binomial probability statement is given below, which is the probability of X being between 20 and 28. Express this probability in words, then apply a continuity correction to convert it into an equivalent normal probability. So, in order to solve this question, we have to recall what we have learned about binomial probability statements, so that we can express our probability statement in words and then apply a continuity correction to convert it into an equivalent normal probability. And so the first step is interpreting the probability in words, which we must identify the variable. Which is X and the compound inequality, which is that X is between 20 and 28, and using this information, we can express our probability in plain language, which gives us the probability that the number of successes X is between 20 and 28 but not including 20 or 28, or we can also say the probability. that the number of successes X is between 21 and 27 inclusive. And now we can apply continuity correction to our statement, which the first step is to recognize the binomial to normal approximation requires adjusting the boundaries by 0.5, which for our probability of X being between the values of A and B, the correct. The form is the probability of X being greater than A + 0.5 and X being less than B minus 0.5. And then we can apply this rule to our probability statement of X being between 20 and 28, which gives us the probability of X being between 20.5 and 27.5. And looking at our answer. Choices, we can identify that answer choice A is the correct answer, as the probability that the number of successes X is between 20 and 28, but not including 20 or 28 when converted into an equivalent normal probability after applying a continuity correction, is the probability that X is between 20.5 and 27.5, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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In Exercises 9–14, write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability.

P(55 < x < 60)

Key Concepts

Binomial Probability

Normal Distribution

Continuity Correction

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In Exercises 9–14, write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability.P(55 < x < 60)