Question

consider the normal distribution defined by the given figure find the mean μ and the standard deviation σ of the distribution μ = kg (simplify your answer.)

Explanation:

Step1: Use the property of normal distribution

In a normal distribution, the mean \(\mu\) is the mid - point of the interval that contains 68% of the data. The formula for the mid - point of an interval \([a,b]\) is \(\mu=\frac{a + b}{2}\), where \(a = 3.8\) and \(b=5.2\).

Step2: Calculate the mean

Substitute \(a = 3.8\) and \(b = 5.2\) into the formula \(\mu=\frac{3.8+5.2}{2}\).

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Answer:

\(4.5\)