SOLUTION: Help I am confused Approximately 25% of the population belongs to a health maintenance organization (HMO). Assume that for a randomly selected group of 20 adults, the number belon

Question 75985: Help I am confused
Approximately 25% of the population belongs to a health maintenance organization (HMO). Assume that for a randomly selected group of 20 adults, the number belonging to an HMO has a binomial distribution.

7. The probability of finding exactly 5 in the 20 who belong to an HMO is:
a. 0.2023
b. 0.1567
c. 0.1750
d. 0.2345

The probability of finding at least one in the 20 who belongs to an HMO is:
a. 0.7500
b. 0.8012
c. 0.9056
d. 0.9968

Thank You
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Approximately 25% of the population belongs to a health maintenance organization (HMO). Assume that for a randomly selected group of 20 adults, the number belonging to an HMO has a binomial distribution.
7. The probability of finding exactly 5 in the 20 who belong to an HMO is:
a. 0.2023
b. 0.1567
c. 0.1750
d. 0.2345
-------
n=20 , p=0.25, x=5
P(x=5)=20C5(0.25)^5(0.75)^15 = 0.20
With a T caluculator it is binompdf(20,0.25,5)
------------------
The probability of finding at least one in the 20 who belongs to an HMO is:
a. 0.7500
b. 0.8012
c. 0.9056
d. 0.9968
------
P(at least one) = 1 - P(x=0)
=1 - 20C0(0.25)^0(0.75)^20
=1 - binompdf(20,0,25,0)
=0.9968...
-------
Cheers,
Stan H.

RELATED QUESTIONS
2. Approximately 20% of the population belongs to a health maintenance organization... (answered by )

2. Approximately 20% of the population belongs to a health maintenance organization... (answered by reviewermath)

A national health organization predicts that 20% of American adults will get the flu... (answered by stanbon)

An employee benefits consulting firm has just completed a survey of the health plans... (answered by stanbon)

A random sample of 20 health maintenance organizations (HMOs) was selected. For each HMO, (answered by Fombitz)

A random sample of health maintenance organizations (HMOs) was selected. For each HMO,... (answered by stanbon)

A random sample of 9 health maintenance organizations (HMOs) was selected. For each HMO,... (answered by Boreal)

a national health organization predicts that 20% of American adults will get the flu... (answered by gmclellan)