Question

1. About 1% of the population has a particular genetic mutation. 200 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 200.

2. A drug test is accurate 97% of the time. If the test is given to 1600 people who have not taken drugs, what is the probability that at least 50 will test positive?

Probability =

Give your answers to at least 3 decimal places.

3. According to the American Red Cross, 9.4% of all Connecticut residents have Type B blood. A random sample of 23 Connecticut residents is taken.

X=X=the number of CT residents that have Type B blood, of the 23 sampled.

What is the standard deviation of the random variable XX?

Answer 1

1. About 1% of the population has a particular genetic mutation. 200 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 200.

p = proportion of the population has a particular genetic mutation = 0.01.

n = sample size = 200

Since the sample is randomly selected from the population. Therefore we can use binomial distribution.

The formula of standard deviation of binomial distribution is as follows :

standard deviation = =  

2. A drug test is accurate 97% of the time. If the test is given to 1600 people who have not taken drugs, what is the probability that at least 50 will test positive?

n = sample size = 1600

here test is given to 1600 people who have not taken drugs. Therefore probability of failure of the test is = 1 - 0.97 = 0.03

Let's use binomial distribution to find the P( X <= 50)

P( X <= 50) = "=BINOMDIST(50,1600,0.03,1)" = 0.650

3. According to the American Red Cross, 9.4% of all Connecticut residents have Type B blood. A random sample of 23 Connecticut residents is taken.
What is the standard deviation of the random variable X .

Let p = proportion of all Connecticut residents have Type B blood = 0.094

n = sample size = 23

Let X=the number of CT residents that have Type B blood, of the 23 sampled.

So that X follows binomial distribution with parameter n = 23 and p = 0.094

the standard deviation of X =