Question

the sample size n, probability of success p, and probability of failure q are given for a binomial experiment. decide whether you can use a normal distribution to approximate the distribution of x.

n = 16, p = 0.89, q = 0.11

can a normal distribution be used to approximate the distribution of x?

a. no, because np < 5 and nq < 5.
b. no, because nq < 5.
c. yes, because np ≥ 5 and nq ≥ 5.
d. no, because np < 5.

Explanation:

Step1: Calculate \(np\)

Given \(n = 16\) and \(p=0.89\), then \(np=16\times0.89 = 14.24\)

Step2: Calculate \(nq\)

Given \(n = 16\) and \(q = 0.11\), then \(nq=16\times0.11=1.76\)

Step3: Check the normal - approximation condition

The condition for using the normal distribution to approximate the binomial distribution is \(np\geq5\) and \(nq\geq5\). Here, \(np = 14.24\geq5\) but \(nq=1.76<5\)

Answer:

B. No, because \(nq < 5\)