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The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of more than 44 correct answers The probability of no more than 35 defective CD's

A) The area to the left of 35
B) The area to the right of 35.5
C) The area to the left of 35.5
D) The area to the left of 34.5

2 Answers

4 votes

Final answer:

The probability of more than 44 correct answers relates to the area to the right of 44.5 due to continuity correction. The probability of no more than 35 defective CDs is represented by the area to the left of 35.5 after the continuity correction. The correct answer to the second part of the question is Option C.

Step-by-step explanation:

The continuity correction is a method used when approximating a discrete distribution, like the binomial distribution, with a continuous distribution such as the normal distribution. When calculating probabilities for discrete occurrences using the normal distribution, half a unit is added or subtracted from the X value depending on the nature of the inequality.

For the question asking about the probability of more than 44 correct answers, you would use an area to the right calculation. Since normal distribution is continuous, and we're simulating it for discrete variables, you would correct this to 44.5 when transitioning from discrete to continuous. This would equate to finding the area to the right of 44.5 on the normal distribution curve.

For the question on the probability of no more than 35 defective CDs, the continuity correction requires us to add 0.5 to the upper limit, yielding 35.5. Therefore, the corresponding region of the normal distribution is the area to the left of 35.5 (Option C). This is because we are interested in the probability of having up to and including 35, which, with the continuity correction, becomes anything less than 35.5.

User OOEric
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Answer:

Option B) The area to the right of 35.5

Step-by-step explanation:

Data:

Let the probability of the correct answers be denoted by the letter C.

The probability of no more than 35 defective CD's can be 35 or less. Therefore, it is presented as follows:

P ≤ 35

Let, the probability of more than 44 correct answers can be presented like this:

P > 44

Therefore, combining the two inequalities gives an area at the right of 35.5

User Obsidian Age
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