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 no more than 35 defective CDs.

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

Question

09-06-2024
Mathematics

High School

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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 no more than 35 defective CDs.

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

Answer :

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JacobWilliamsJr JacobWilliamsJr · Answer 1 · 2023-08-03T08:43:42-04:00

The correct answer is the area to the left of 35.5 (option B) because of the continuity correction applied to the discrete count of 35 for defects. Therefore, the correct option is B.

The question involves using the continuity correction when approximating a discrete distribution with a continuous normal distribution. Since the student is interested in the probability of no more than 35 defective CDs, this means we are looking for the area to the left of 35 in the normal distribution.

However, to incorporate the continuity correction, we should adjust this value by 0.5, because a discrete count of 35 contains values up to and including 35. Thus, the correct option will include 35 plus 0.5 for the continuity correction.

Therefore, the area under the normal distribution curve that represents this probability is the area to the left of 35.5. The correct answer is option B) The area to the left of 35.5.