IB Maths SL Normal DistributionAnswers
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
b). Given that 10% of the girls are shorter than x cm, find x.Answer
Here you have inverse normalBy GDC (Casio)
menu>STAT>DIST>NORM>InvN with Tail:Left, Area:0.1, sigma=10, mu=155 and you get
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
Again you have an inverse normal caseBy 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
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!!
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