Thus the probability that a randomly selected woman from this university is 67.5 inches or taller is 0.16
Let x be the height of the woman. Mean height of women μ = 65 inches
Standard deviation σ = 2.5 inches
By theorem if X ~ N( 65 , 2.5² )
then normal distribution Z = X - μ / σ ~ N(0,1)
68% of women have a height that falls within 1 standard deviation of the mean. That is P ( 62.5 ≤X ≤ 67.5) = 0.68
From symmetry and using probability, we can find the area under the bell-shaped curve for this interval. This area to the right of 67.5 under the bell-shaped curve ultimately gives us that the probability a randomly selected woman from the university is 67.5 inches or taller. This probability = 0.16
More information about bell-shaped curves brainly.com/question/28235963
#SPJ4
