4.36 Among American women aged 20-29yrs, 10% are less than 60.8inches tall, 80%

Question

4.36

Among American women aged 20-29yrs, 10% are less than 60.8inches tall, 80% are between 60.8 and 67.6 inches tall and 10% aremore than 67.6 inches tall. Assuming that the height distributioncan be adequately approximated by a normal curve, find the mean andstandard deviation of the distribution.

Explanation / Answer

Let X be the height of a women, then X follows normal distribution, so X ~ N ( a , b) . We need to find a and b, also if Z = (X - a) /b , then Z ~ N(0 ,1) Now, we are given : P [ X < 60.8 ] = 0.1  ; P[ 60.8 67.6 ] = 0.1 Now,   P [ X < 60.8 ] =0.1        or,   P [ (X - a) /b < (60.8 - a) / b ] = 0.1   => (60.8 - a) /b =-1.282             ............ (1)           (using tables) also,      P[ X > 67.6 ] =0.1      or,   P [ (X - a) /b > (67.6 - a) / b ] = 0.1   => (67.6 - a) /b =1.282             ............ (2)           (using tables) using (1) and (2) , we get : a = 64.2 , b = 2.65

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.