In a hospital, the probability of male births is 0.4. a) What is t

Pearl Carney

Pearl Carney

Answered question

2021-11-19

In a hospital, the probability of male births is 0.4.
a) What is the probability that the number of female births is 9 in the next 20 births?
b) What is the probability that the number of female births is less than 18 in the next 20 births?

Answer & Explanation

Ancessitere

Ancessitere

Beginner2021-11-20Added 17 answers

Step 1
Solution:
Let X be the number of female births and n be the sample number of births.
From the given information, probability of male birth is 0.40 and n=20. The probability of female birth is 10.40=0.60.
Step 2
Here, births are independent and probability of success is constant. Hence, X follows binomial distribution with parameters n=20 and p=0.60.
The probability mass function of binomial random variable X is
P(X=x)=(nx)px(1p)nx;x=0,1,....,n
Step 3
a. The probability that the number of female births is 9 in the next 20 births is
P(X=9)=(209)0.609(10.60)209
=0.0710
The probability that the number of female births is 9 in the next 20 births is 0.0710.
Step 4
b. The probability that the number of female births is less than 18 in the next 20 births is
P(X<18)=P(X17)
=0.9964 [Using the excel function =BINOM.DIST (17,20,0.6,TRUE]
The probability that the number of female births is less than 18 in the next 20 births is 0.9964.

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