Question

Approximately 15% of Americans have a blood type of B. The local blood bank has 80 donors stop by on a given day (which can be considered a random sample from the population). What is the probability that between 15% and 20% of the donors on a given day have a blood type of B? Be sure to state and justify your assumptions.

Answer 1

So I can justify the fact that this is normal, since there is a large sample size. That's all I got, though.

Answer 2

Use the binomcdf function on a calculator. 15% of 80 is 12 and 20% of 80 is 16. Plug in binomcdf(80,0.15,11) to find the P(X<12) which is .45219. Then plug in binomcdf(80,0.15,16) to find the P(X≤16) which is .91629. Subtract P(X<12) from P(X≤16) to get P(12≤x≤16) which is .46410. So the probability that between 15% and 20% (12 people and 16 people) have blood type B is about 0.46410.

Answer 3

Thank you. I had one more question. If you could help me with that, that'd be great!!

An opinion poll asks an SRS of 1500 adults, "Do you happen to jog?" Suppose that the population proportion who jog (a parameter) is p = 0.15. To estimate p, we use the proportion p-hat in the sample who answer "Yes." Justify the use of a normal approximation and find the following probabilities.

a) P(p > 0.16)

b) P(0.14 < p < 0.16)

Answer 4

Again, I can justify the normal approximation, but I have trouble with the actual probabilities.

Answer 5

Use z distributions for answering the question.
z=(O - E)/SEp
O is the observed proportion for p-hat
E is the expected proportion or p
SEp is the standard error of the sample proportion =√(p*(1-p)/n)

a) z=(0.16 - 0.15)/0.0092=+1.09 so P(p>0.16) is P(z>1.09)
This means you have to find the probability a number is 1.09 standard deviations above the mean. In a normal distribution, this means how much of the area is above 1.09 standard deviations from the mean. This is 0.138

b) Using the same steps as part a, convert the probability into P(-1.09<z<1.09). This means how much of the area is between -1.09 standard deviations from the mean and +1.09 standard deviations from the mean. This is 0.724

Answer 6

I see!! Thank you!!!!