Question

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?

Answer 1

Answer:

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;

$P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......$

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)  =  $n \times p$

                 =  $26 \times 0.103$  = 2.678

Answer 2

The expected value of the random variable X is 2.678.

Important information:

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.

Calculation of expected value:

= 26 (10.3%)

= 2.678

Here we multiplied the random sample with the given percentage so that the expected value could come.

Learn more about the variable here: https://brainly.com/question/21444495