Advanced Placement Statistics: Randomness and Simulations

Question

Homework Help Please. This has me stumped

A person with type O blood can donate red blood cells to anybody because type O blood is the universal donor blood type. About 44% of the US population has type O blood. You are asked to design a simulation to determine the probability that at least 3 of 10 people will have type O blood.

Part A: Conduct five trials using the following table of random digits:

96299	07196	98642	20639	23185	56282	69929	14125	38872	94168
71622	35940	81807	59225	18192	08710	80777	84395	69563	86280
03272	41230	81739	74797	70406	18564	69273	72532	78340	36699
46376	58596	14365	63685	56555	42974	72944	96463	63530	24152
47352	04266	74017	79319	70170	96572	08523	56025	89077	57678

Part B: Based on your simulation, what is the probability that at LEAST 3 of 10 people will have type O blood?

Answer 1

Hey James! Since we know that 44% of the population has Type O blood, we will assign the values of 00 through 43 (which includes 44 of the 100 two digit numbers...since we start at 00 the hundredth number will be 99) to represent a person with Type O blood.

We then use this table of random digits to conduct the five trials, each containing ten subjects. In our first trial, we get (going horizontally in the table):

96, 29, 90, 71, 96, 98, 64, 22, 06, 39

which tells that in our first of the five trials, four people have Type O blood (29, 22, 06, and 39). We then complete the next trial, beginning with the next number in the table which is 23. You then continue this for five trials.

In Part B, you need to determine how many of your trials resulted in 3 or more people who have Type O blood and then give your answer as a percentage. I'll let you do this yourself, but for example, if you found that this was the case for 2 of your 5 trials, your answer for Part B would be 2/5 = 0.4. This answer is based only on YOUR simulation using THIS table of random digits (but could vary even if you found another valid way of randomly selecting members of the population as you conducted another five trials).