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The heights of women aged 20 to 29 follow approximately the N(64, 2.82) distribution. Men the same age have heights distributed as N(69.3, 2.71). What percent of young women are shorter than the mean height of young men?

Respuesta :

Answer:96.97

Step-by-step explanation:

Given

mean height of women [tex]\mu _w=64[/tex]

Standard deviation of height [tex]\sigma _w=2.82[/tex]

mean height of men [tex]\mu _=69.3[/tex]

Standard deviation of height [tex]\sigma _m=2.71[/tex]

P[tex]\left ( X<69.3\right )[/tex]

P[tex]\left ( \frac{x-\mu _w}{\sigma _w}\right )<P\left ( \frac{69.3-64}{2.82}\right )[/tex]

P[tex]\left ( Z<1.8794\right )[/tex]

i.e. 0.9697=96.97 %