Question

a medical device company knows that the percentage of patients experiencing injection - site reactions with the current needle is 11%. what is the standard deviation of x, the number of patients seen until an injection - site reaction occurs?
3.1289
8.5763
9.0909
11

Explanation:

Step1: Identify the distribution

The random variable \(X\) (number of patients seen until an injection - site reaction occurs) follows a geometric distribution. For a geometric distribution, the probability of success \(p = 0.11\) (where success is an injection - site reaction).

Step2: Recall the formula for the standard deviation of a geometric distribution

The formula for the standard deviation of a geometric distribution is \(\sigma=\sqrt{\frac{1 - p}{p^{2}}}\).

Step3: Substitute \(p = 0.11\) into the formula

First, calculate \(1-p=1 - 0.11 = 0.89\). Then, \(\frac{1 - p}{p^{2}}=\frac{0.89}{0.11^{2}}=\frac{0.89}{0.0121}\approx73.5537\).

Step4: Calculate the square - root

\(\sigma=\sqrt{\frac{1 - p}{p^{2}}}=\sqrt{73.5537}\approx8.5763\)

Answer:

B. \(8.5763\)