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 = 19, p = 0.94, q = 0.06

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

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

Explanation:

Step1: Calculate \(np\)

\(np = 19\times0.94=17.86\)

Step2: Calculate \(nq\)

\(nq = 19\times0.06 = 1.14\)

Since \(nq=1.14<5\), we check the condition for normal - approximation to binomial (\(np\geq5\) and \(nq\geq5\)).

Answer:

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