this is a table below
blood type percent
O 46
A 42
B 9
AB 3
If 120 people are donating blood, what is the expected number of people with type o blood? Why would this be considered a binomial distribution? b) Calculate the expected number of people with each of the other types of blood.
To answer these questions, we need to understand binomial distribution. A binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials (where each trial has only two possible outcomes - success or failure) under the assumption of constant probability of success.
In this case, we can consider each person donating blood as an independent Bernoulli trial, where the outcome is either having blood type O or not having blood type O.
To answer the first question, the expected number of people with type O blood can be found by multiplying the probability of having type O blood (given as 46%) by the total number of people donating blood (given as 120):
Expected number of people with type O blood = Probability of having type O blood x Total number of people donating blood
= 46% x 120
= (46/100) x 120
= 55.20
So, the expected number of people with type O blood is 55.20.
For the second question, to calculate the expected number of people with each of the other types of blood (A, B, and AB), we can follow the same approach:
Expected number of people with type A blood = Probability of having type A blood x Total number of people donating blood
= 42% x 120
= (42/100) x 120
= 50.40
Expected number of people with type B blood = Probability of having type B blood x Total number of people donating blood
= 9% x 120
= (9/100) x 120
= 10.80
Expected number of people with type AB blood = Probability of having type AB blood x Total number of people donating blood
= 3% x 120
= (3/100) x 120
= 3.60
Therefore, the expected number of people with type A blood is 50.40, with type B blood is 10.80, and with type AB blood is 3.60 in a sample of 120 people donating blood.