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How to find percentiles of a Normal distribution?

The weight of a given Africander breed is said to follow a normal distribution with mean 200 kg and standard deviation of 10. Calculate a) The probability that the weight of the Africander is less than 215 kg.

b) The probability that the weight lies between 190 kg and 210 kg.

c) Find the weight M kg such that the probability of X > M = 5%

d) Given that there are 10 Africander whose weights are greater than M kg, Calculate the probability that there are exactly 2 Africanders whose weights are greater than M kg.

  • $\begingroup$ Probably should label as homework. $\endgroup$ Commented Aug 31, 2012 at 16:10
  • $\begingroup$ maxwell, please research our site first and then come back if you have specific difficulties solving these problems. $\endgroup$
    – whuber
    Commented Aug 31, 2012 at 16:52

1 Answer 1


All these answers can be found by using a table of the N(0,1) (standard normal) distribution. When you are given the weight say X then you calculate Z=(X-200)/10. So for example in a) you want P(X>215)= P(Z>(215-200)/10=1.5). So you look up P(Z>1.5 in the standard normal table.

For b) you want P(210 > X > 190)=P(1 > Z > -1).

For c) you want P(Z > u)=1-P(Z < u)=0.05 so you look up u and then since u=(M-200)/10



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