SOLUTION: according to a study conducted approximately 55% of all hospitals in a given town contained 100 or more beds. A researcher draws a sample of 15 hospitals by randomly selecting name

Question 1205803: according to a study conducted approximately 55% of all hospitals in a given town contained 100 or more beds. A researcher draws a sample of 15 hospitals by randomly selecting names from a directory of hospitals.
A.What is the probability of selecting 10 or more hospitals that have 100 or more beds?
B.What is the probability of selecting less than five hospitals that have 100 or more beds?
C.What is the probability of selecting from six to ten hospitals, inclusive, that have 100 or more beds?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this looks like a binomial probability distribution type of problem.

the formula is p(x) = p^x * q^(n-x) * c(n,x).

n is 15
x is from 0 to 15
p = .55
q = (1-.55)
c(n,x) = n! / (x! * (n-x)!

probabilities are shown in the excel printout below:

the sum of all probabilities is p(x) from 0 to 15 and is equal to 1, as it should be.

answers to your questions are:

A. What is the probability of selecting 10 or more hospitals that have 100 or more beds?

p(10 or more) = sum p(x) for x = 10 to 15 = 0.260759769

B. What is the probability of selecting less than five hospitals that have 100 or more beds?

p(less than 5) = sum p(x) for x = 0 to 4 = 0.025465853

C. What is the probability of selecting from six to ten hospitals, inclusive, that have 100 or more beds?

p(6 to 10) = sum(p(x) for x = 6 to 10 = 0.802671982

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