Recall that the standard normal distribution table gives the cumulative area to the left of the z-score. 01% percentage of women who are too tall is the same because z score is 6.72 =. =.00010 To find the percentage of men that are taller than 80 in, convert 0.0001 to a percent. Use a normal distribution table to find the cumulative area to the left of z=4.04 =.9999 -now subtract the area 0.9999 from 1 to find the area of the shaded region. To find the area under the curve to the right of the z-score subtract the cumulative area to the left of the z-score from 1. Use the fact that z=(x−μ)/σ (80 - 68.7) / 2.8 = 4.04 Recall that the area under the normal curve is equal to 1. The next step is to convert 80 to its corresponding z score.
/Z-dc7881981d5b4ab5a8765f2a293c9552.png "standard normal distribution z score table")
In order to determine what percentage of men are too tall to fit through the doorway without bending, draw a standard normal curve. The area below the normal curve represents a proportion or probability. Suppose that a random variable x is normally distributed with mean μ and standard deviation sσ.
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