SOLUTION: Help Please! This is my last math course and I'm afraid it will ruin my bursury. All the rest of my marks are in the high 80's and 90's. But math is a struggle for me . . .

Question 453907: Help Please!
This is my last math course and I'm afraid it will ruin my bursury. All the rest of my marks are in the high 80's and 90's.
But math is a struggle for me . . .

A new drug has been tested and is found to have a cure rate of 80%. The drug is given to a random sample of 100 patients for a further test. Using a normal approximation to the binomial distribution, find the probability that:
a) at least 75 patients will be cured
b) exactly 80 patients will be cured
Thank you so much.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A new drug has been tested and is found to have a cure rate of 80%.
The drug is given to a random sample of 100 patients for a further test.
Using a normal approximation to the binomial distribution, find the probability that:
a) at least 75 patients will be cured
mean = np = 100*0.80 = 80
std = sqrt(npq) = sqrt(80*0.2) = 4
---
z(74.5) = (74.5-80)/4 = -1.1
z(100.5) = (100.5-80)/4 = 20.5/4 = 5.125
----------------
P(75<= x <=100) = P(-1.1< z < 5.125) = 0.8643
======================================================
b) exactly 80 patients will be cured
z(79.5) = (79.5-80)/4 = -0.125
z(80.5) = (80.5-80)/4 = +0.125
---
P(x = 80) = P(-0.125< z <0.125) = 0.0995
=========================
Cheers,
Stan H.
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