Question

A new antibiotic is effective for 85% of infections. The antibiotic is given to 40 patients.
a) Verify that this is a binomial setting and write it in notation.
b) Describe what P(X=35) means in context.
c) What is the probability that the antibiotic will work in at least 35 of the 40 patients?
d) What is the probability that the antibiotic will work in less than half of the patients?

Answer 1

@campbell_st

Answer 2

1) It works or it doesn't. Seems like it might be binomial.
2) Only 40 patients. Oh, well that's finite. Binomial it is!

Answer 3

huh?

Answer 4

well if its binomial probability then you will need to use

Part 1
\[P(k- successes-and- (n - k)- failures) = ^{n}C_{k} p^kq^{n - k}\]

so p = 0.85 and q = 0.15 and n = 40

so to prove it 0.85 + 0.15 = 1

Part 2

P(X = 35) is the probability that 35 people have an effective drug..

Part 3

find the probabilities of X = 35 and greater and add them together.

P( X >= 35) = P(35) + P(36) + P(37) + P(38) + P(39) + P(40)

hope this helps.

Answer 5

How would I find d??

Answer 6

the thing that makes it binomial is that there are only 2 outcomes... the drug is effective, or it not effective....

effective = 0.85, not effective = 0.15

Answer 7

I have this:

(a) p = 0.85 and q = 0.15 and n = 40

To prove it: 0.85 plus 0.15 = 1

(b) P(X = 35) is the probability that 35 people have an effective drug.

(c) P( X >= 35)
= P(35) plus P(36) plus P(37) plus P(38) plus P(39) plus P(40)

(d)

**effective = 0.85, not effective = 0.15**

Answer 8

(d) ?

Answer 9

without much thought it might be

1 - P(X >= 20)

which seems a lot of calculating...

Answer 10

(a) p = 0.85 and q = 0.15 and n = 40

To prove it: 0.85 plus 0.15 = 1

(b) P(X = 35) is the probability that 35 people have an effective drug.

(c) P( X >= 35)
= P(35) plus P(36) plus P(37) plus P(38) plus P(39) plus P(40)

(d) 1 - P(X >= 20)

**effective = 0.85, not effective = 0.15**

Answer 11

does that look good/ ^^

Answer 12

it makes sense but part (d) seems very tedious...
hope it helps..