According to the american red cross, 10.3% of all connecticut residents have type b blood. a random sample of 26 connecticut residents is taken. X= the number of CT residents that have Type B blood, of the 17 sampled. What is the expected value of the random variable X?

The expected value of the random variable X is 2.678.

Step-by-step explanation:

We are given that according to the American red cross, 10.3% of all Connecticut residents have type B blood.

Also, a random sample of 26 Connecticut residents is taken.

Let X = the number of CT residents that have Type B blood

The above situation can be represented through binomial distribution;

where, n = number of trials (samples) taken = 26 residents

            r = number of success

            p = probability of success which in our question is % of all  

                  Connecticut residents who have type B blood, i.e; 10.3%.

So, X ~ Binom(n = 26, p = 0.103)

Now, the expected value of the random variable X is given by;

        E(X)  =  

                 =    = 2.678