Question

In: Statistics and Probability

1. Every two seconds someone in America needs blood. It is important that hospitals have the...

1. Every two seconds someone in America needs blood. It is important that hospitals have the right types of quality
blood to meet the patient needs. Blood donation centers help hospitals meet this demand. There are four main
blood groups: A, B, AB, and O, of which O is the most common. One of the less common blood types is B+. In
the United States, only 9% of the population has B+ blood type.
Assume that 5 donors arrive to a blood donation center and you are interested in the number of these donors that
have B+ blood type. Therefore, let X be the random variable that represents the number of donors with B+ blood

a) What type of distribution is the random variable X?
b) CENTRAL TENDENCY: Calculate the mean of X
c) DISPERSION OR SPREAD: Calcuate the variance and standard deviation of X
d) SHAPE: Create the probability mass function of X in graphical format
e) SHAPE: Create the cumulative distribution function of X in graphical format.
type among the 5 donors that came to the center.

Expert Solution

1. The proportion of the population has B+ blood type is p=0.09

Assuming that 5 arrived to a blood donation centre.

Let X be the random variable that represents the number of donors with B+ blood.

a. Therefore the distribution of X is binomial with parameter n=5 and p=0.09

Since probability of success is constant and sample size is fixed. Also the trials are independent, that is the blood group of each person is independent of each other.

b. The mean of random variable X is

c. The variance of random variable X is:

The standard deviation is

d.

orchestra answered 1 year ago

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