We have been told that the random variable is normally distributed with a mean of μ = 16.4 and a standard deviation of σ = 2.6. We want to find the range of values that represent the middle 95 % of the distribution.
P(aP(μ-z < X < μ + z) = 95 %
Let's recall the Empirical Rule for the normal distribution. According to this rule, approximately 95 % of the data fall within 2σ from the mean.
P(μ - 2σ < X < μ + 2σ) = 95 %
Knowing that μ=16.4 and σ=2.6, let's find both ends of the range.
We found the range that represents the middle 95 % of the distribution.
P( 11.2 < X < 21.6 ) = 95 %
We can now use the Empirical Rule to help us visualize the data with these parameters. Let's shade the areas that satisfy the compound inequality 11.2
