4.-/4 pointsBBBasicStat7 7.1.007. Assuming that the heights of college women are

Question

4.-/4 pointsBBBasicStat7 7.1.007. Assuming that the heights of college women are normally distributed with mean 70 inches and standard deviation 2.2 inches, answer the following questions. (Hint: Use the figure below with mean and standard deviation .) Area Under a Normal Curve 10-047-i) 16-2.2 2.35%/ 13.5% | 34% | 34% | 13.5% 2.35% ( 68% 95% 99.7% 2.35 4945 (a) What percentage of women are taller than 70 inches? (b) What percentage of women are shorter than 70 inches? (c) What percentage of women are between 67.8 inches and 72.2 inches? (d) What percentage of women are between 65.6 and 74.4 inches? 34 Talk to a Tutor 5. -/1 points8BBasicStat? 7.2.003. What is the value of the standard score for the mean of a distribution? Need Help?ReaTalk to a Tutor

Explanation / Answer

According to the Empirical Rule 68-95-99.7
Mean +/- 1*SD covers 68%
Mean +/- 2*SD covers 95% and
Mean +/- 3*SD covers 99.7% of the values
Further,
Percentage of values below the Mean = Percentage of values above the Mean = 50%
z = (X-Mean)/SD

a) Required percentage = 50%
b) Required percentage = 50%

[70 being the Mean] std =2.2
c) z1 = (67.8 - 70)/2.2 = - 1
z2 = (72.2 - 70)/2.2 = + 1
Therefore, Required percentage = 68%

d) z1 = (65.6 - 70)/2.2 = - 2
z2 = (74.4- 70)/2.2 = + 2
Therefore, Required percentage = 95%

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