Chardonnay Felix

2021-02-25

Basic Computation:$\stackrel{^}{p}$ Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(b) Suppose $n=25$ and $p=0.15$. Can we safely approximate the $\stackrel{^}{p}$ distribution by a normal distribution? Why or why not?

Benedict

Expert

We have binomial experiment with $n=25$ and $p=0.15$
$np=25\left(0.15\right)$
$np=3.75$
$nq=25\left(1-0.15\right)$
$nq=21.25$
Since both the values np and nq are not greater than 5, hence, we cannot approximate the $\stackrel{^}{p}$ distribution by a normal distribution.

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