Chapter 6.3, Problem 105E

To determine

To calculate; the appropriate option, that can be used to approximate binomial distribution using normal distribution.

Answer to Problem 105E

The right answer is (c)

Explanation of Solution

The required conditions approximate binomial distribution using normal distribution are:

  $\begin{array}{l}np\ge 10\\ nq\ge 10\end{array}$

  $\begin{array}{l}\text{(a) np = 10(0}\text{.5) = 5, nq = n(1 - p) = 10(1 - 0}\text{.5) = 5}\\ \text{(b) np = 40(0}\text{.88) = 35}\text{.2, nq = n(1 - p) = 40(1 - 0}\text{.88) = 4}\text{.8}\\ \text{(c) np = 100(0}\text{.2) = 20, nq = n(1 - p) = 100(1 - 0}\text{.2) = 80}\\ \text{(d) np = 100(0}\text{.99) = 99, nq = n(1 - p) = 100(1 - 0}\text{.99) = 1}\\ \text{(e) np = 1000(0}\text{.003) = 3, nq = n(1 - p) = 1000(1 - 0}\text{.003) = 997}\end{array}$

As the require condition are only met in option (c), therefore, the right answer is option (c).