Question

It's been estimated that during "needlestick" accidents involving HIV positive individuals, there is a probability of approximately 3/1000 that HIV will be transmitted to the injured person. Suppose a health care worker suffers 15 needlestick injuries with HIV-positive patients. Find the probability that the worker will not be infected with HIV as a result of these 15 needlesticks.

Let X = the number of needlesticks needed for the first HIV infection to occur.

Find the mean and standard deviation of X.

Mean of X =

Standard Deviation of X =

Answer 1

Answer:

Given that:

It's been estimated that during "needlestick" accidents involving HIV positive individuals, there is a probability of approximately 3/1000 that HIV will be transmitted to the injured person.

This is a case o binomial distribution as n is constant, p = 0.003 is same for all,Only two outcomes and events are independent.

Here we need to find P(x = 0) = BINOM.DIST(0,15,0.003,0)

= 0.9559

Now for binomial distribution mean

Standard deviation =