In a survey of women in a certain country (ages 20minus29), the mean height was 64.3 inches with a standard deviation of 2.77 inches. Answer the following question about the specified normal distribution. (a) What height represents the 95th percentile
Accepted Solution
A:
Answer: 68.86 inchesStep-by-step explanation:Given : In a survey of women in a certain country having Mean : [tex]\mu=64.3\text{ inches}[/tex]Standard deviation : [tex]\sigma=2.77\text{ inches}[/tex]The z-value corresponds to 0.095 is 1.645. [Using standard normal distribution table]The height that represents the 95th percentile is given by :-[tex]H=z\times\sigma+\mu\\\\=1.6449\times2.77+64.3=68.856373\approx68.86\text{ inches}[/tex]Hence, the height represents the 95th percentile = 68.86 inches.