Normal distribution mean is 15, SD is 3 interval covers 95% of value

To find the interval that covers 95% of the values in a normal distribution, we use the Empirical Rule. For a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean. Given: Mean (μ) = 15; Standard Deviation (σ) = 3 Step 1: Calculate the lower bound of the interval. Lower bound = μ − 2σ; Lower bound = 15 − (2 × 3); Lower bound = 15 − 6; Lower bound = 9 Step 2: Calculate the upper bound of the interval. Upper bound = μ + 2σ; Upper bound = 15 + (2 × 3); Upper bound = 15 + 6; Upper bound = 21 The interval that covers 95% of the values is (9, 21).

Normal distribution mean is 15, SD is 3 interval covers 95% of value

To find the interval that covers 95% of the values in a normal distribution, we use the Empirical Rule. For a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean. Given: Mean (μ) = 15; Standard Deviation (σ) = 3 Step 1: Calculate the lower bound of the interval. Lower bound = μ − 2σ; Lower bound = 15 − (2 × 3); Lower bound = 15 − 6; Lower bound = 9 Step 2: Calculate the upper bound of the interval. Upper bound = μ + 2σ; Upper bound = 15 + (2 × 3); Upper bound = 15 + 6; Upper bound = 21 The interval that covers 95% of the values is (9, 21).

Solved: Normal distribution mean is 15, SD is 3 interval…

To find the interval that covers 95% of the values in a normal distribution, we use the Empirical Rule. For a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean.

Given:

Mean (μ) = 15
Standard Deviation (σ) = 3

Calculate the lower bound of the interval.
Lower bound = μ - 2σ
Lower bound = 15 - (2 × 3)
Lower bound = 15 - 6
Lower bound = 9
Calculate the upper bound of the interval.
Upper bound = μ + 2σ
Upper bound = 15 + (2 × 3)
Upper bound = 15 + 6
Upper bound = 21

The interval that covers 95% of the values is (9, 21).

Normal distribution mean is 15, SD is 3 interval covers 95% of value

Step-by-step solution

Calculate the lower bound of the interval.

Calculate the upper bound of the interval.

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