SOLUTION: in a survey of women in a certain country​ (ages 20minus​29), the mean height was 63.7 inches with a standard deviation of 2.73 inches. Answer the following questions a

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Question 1120470: in a survey of women in a certain country​ (ages 20minus​29), the mean height was 63.7 inches with a standard deviation of 2.73 inches. Answer the following questions about the specified normal distribution.
​(a) What height represents the 95th ​percentile?
​(b) What height represents the first​ quartile?
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
a) z-score for the 95% is 1.64
:
1.64 = ( X - 63.7 ) / 2.73
:
X - 63.7 = 1.64 * 2.73 = 4.4772
:
X = 63.7 + 4.4772 = 68.1772 approximately 68.2 inches
:
b) z-score for 25% is -0.68
:
-0.68 = ( X - 63.7 ) / 2.73
:
X - 63.7 = -0.68 * 2.73 = -1.8564
:
X = 63.7 - 1.85664 = 61.8436 approximately 61.8 inches
:
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