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Forty percent of the values in a normal distribution are at least k. Which area do you look up to find k?
AAn area of 0.60 to the left
BAn area of 0.40 to the left
CAn area of 0.40 to the right
DAn area of 0.20 to the left
Answer & Solution
Correct answer: A. An area of 0.60 to the left
1. The phrase at least means greater than or equal to, so it describes the right-hand side.
2. That puts an area of 0.40 to the right of k.
3. The whole area under the curve is 1.
4. So the area to the left of k is 1 minus 0.40.
5. That gives an area of 0.60 to the left of k.
6. A table indexed by left-hand areas is then read at 0.60.
7. Looking up 0.40 on the left would find the value with only 40 percent below it.
8. Looking up 0.40 on the right is the right idea but the wrong table, since most tables report left-hand areas.
_Source: OpenStax High School Statistics (CC BY 4.0), Ch 6 "The Normal Distribution", section 6.2 Using the Normal Distribution_
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