Normal Distribution

Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths SL Revision Notes

Normal Distribution

Postby judIB » Sun Jul 07, 2013 6:12 pm

Question:
1. In a large school, the heights of all fourteen-year-old students are measured. The heights of the girls are normally distributed with mean 155cm and standard dev. 10cm. The heights of the boys are normally distributed with mean 160cm and standard dev. 12 cm.
a). Find the probability that a girl is taller than 170cm.
b). Given that 10% of the girls are shorter than x cm, find x.
c). Given that 90% of the boys have heights between qcm and rcm where q and r are symmetrical about 160cm, and q<r, find the value of q and of r.

In the group of 14 year old students, 60% are girls and 40% are boys.
The probability that a girl is taller than 170cm was found in part (a).
The probability that a boy is taller than 170cm is 0.202

A 14 year old student is selected at random.
d). Calculate the probabilitt that the student is taller than 170cm.
e). Given that the student is taller than 170cm, what is the probability the student is a girl?

Thanks!
judIB
 
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IB Maths SL Normal Distribution

Postby miranda » Mon Jul 08, 2013 12:36 pm

IB Maths SL Normal Distribution
Answers:
1. In a large school, the heights of all fourteen-year-old students are measured. The heights of the girls are normally distributed with mean 155cm and standard dev. 10cm. The heights of the boys are normally distributed with mean 160cm and standard dev. 12 cm.
a). Find the probability that a girl is taller than 170cm.
Answer:
By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:170, Upper:9*10^99, sigma=10, mu=155 and you get
P(G>170)=0.0668072


b). Given that 10% of the girls are shorter than x cm, find x.

Answer:
P(G<x)=0.1
Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Left, Area:0.1, sigma=10, mu=155 and you get
x=142.184484

c). Given that 90% of the boys have heights between qcm and rcm where q and r are symmetrical about 160cm, and q<r, find the value of q and of r.

Answer:
P(q<B<r)=0.9

Again you have an inverse normal case

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Central, Area:0.9, sigma=12, mu=160 and you get
q=140.261756 and r=179.738244




In the group of 14 year old students, 60% are girls and 40% are boys.
The probability that a girl is taller than 170cm was found in part (a).
The probability that a boy is taller than 170cm is 0.202

A 14 year old student is selected at random.
d). Calculate the probability that the student is taller than 170cm.

Answer:
P(S>170)=0.6*P(G>170)+0.4*P(B>170)=0.12088432

e). Given that the student is taller than 170cm, what is the probability the student is a girl?

Answer:
P(G/taller than 170)=P(Girl AND taller than 170)/P(taller than 170)=(0.6*0.0668072)/0.12088432=0.33159


Hope these Help!! :) :)

Take a look at the following posts

ib-mathematics-sl-normal-distribution-t200.html
ib-math-sl-normal-distribution-t198.html
ib-maths-sl-normal-distribution-t197.html
miranda
 
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