Math  /  Data & Statistics

QuestionThree Normal distributions all have mean 20. Distribution A has standard deviation 1, distribution B has standard deviation 5, and distribution CC has standard deviation 10. The distribution with the flattest peak is \qquad Distribution A Distribution C Distribution B They will all have the same shape.

Studdy Solution

STEP 1

1. The problem involves three Normal distributions, each with the same mean but different standard deviations.
2. The mean does not affect the shape of the distribution, but the standard deviation does.
3. The standard deviation of a Normal distribution affects the spread and peak of the distribution.

STEP 2

1. Understand the relationship between standard deviation and the shape of a Normal distribution.
2. Compare the standard deviations of the given distributions.
3. Identify which distribution has the largest standard deviation, as it will have the flattest peak.

STEP 3

Understand the relationship between standard deviation and the shape of a Normal distribution.
The standard deviation (σ\sigma) of a Normal distribution affects its spread. A larger standard deviation results in a wider spread and a flatter peak, while a smaller standard deviation results in a narrower spread and a sharper peak.

STEP 4

List the standard deviations of the given distributions:
- Distribution A: σA=1\sigma_A = 1 - Distribution B: σB=5\sigma_B = 5 - Distribution C: σC=10\sigma_C = 10

STEP 5

Compare the standard deviations to determine which distribution has the largest standard deviation.
σC=10>σB=5>σA=1 \sigma_C = 10 > \sigma_B = 5 > \sigma_A = 1

STEP 6

Conclude that the distribution with the largest standard deviation will have the flattest peak.
Thus, Distribution C, with σC=10\sigma_C = 10, will have the flattest peak.
Solution: The distribution with the flattest peak is Distribution C.

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