The probability of a lady over 40 years of age not having had children is 0.1. In a sample of 60 ladies over 40, what are the chances that between 5 and 9 of them have had no children?

Question

I answered the question Using binomial distribution and got,

#P(5 < x < 9)=0.656#

This is close to the answer but wrong.

Can you explain why we use Z scores and normal distribution to work it out when it is binomial?

Thanks,

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Answer 1 · 2016-12-22T06:14:43

The chances that between 5 and 9 of them have had no children#=0.2909#

In such problems, it is always better to use Normal Probability distribution as an approximation to Binomial Distribution.

The conditions you have to apply before using this method is this

#np= >5#
and
#nq= >5#

If these two conditions are satisfied you can apply Normal Probability distribution in the place of Binomial Distribution.

Why should we use the Normal Probability Distribution instead of Binomial Distribution.

Using the formula #"_nC_r*p^r*q^(n-r)# is very difficult if not impossible. For example -

#"_60C_6=50063860#. This is very very combersome.

Now the answer

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