a medical device company knows that the percentage of patients experiencing injection - site reactions with…

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?\n3.1289\n8.5763\n9.0909\n11

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?\n3.1289\n8.5763\n9.0909\n11

Answer

Answer:

C. 9.0909

Explanation:

Step1: Identify the distribution

This is a geometric - distribution problem. In a geometric distribution, the probability of success $p = 0.11$.

Step2: Recall the formula for standard deviation

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

Step3: Substitute the value of $p$

Substitute $p = 0.11$ into the formula. First, calculate $1 - p=1 - 0.11 = 0.89$. Then, $p^{2}=(0.11)^{2}=0.0121$.

Step4: Calculate the standard deviation

$\sigma=\sqrt{\frac{0.89}{0.0121}}=\sqrt{73.5537}\approx9.0909$.