Question

What is the probability that out of 60 lambs born on BaaBaa Farm, at least 35 will be male? Assume that males and females are equally probable, and round your answer to the nearest tenth of a percent.

A. 12.3%
B. 4.6%
C. 25.9%
D. 44.9%

Answer 1

A. 12.3%

Explanation:

Model this as a binomial distribution

`X \sim B(n,p)` where X is the random variable, n is the number of trials, and p is the probability of success.

Therefore,

• X = lambs born male
• n = 60
• p = 0.5

(If the probability of lambs being male and female is equal, then the probability of males being born = 0.5)

`X \sim B(60,0.5)`

The probability that at least 35 lambs will be born male:

`\ \ \ \ \ \ \ P(X\geq 35)=1-P(X\leq 34)\\\\\implies P(X\geq 35)=1-0.8774695851...\\\\\implies P(X\geq 35)=0.1225304149\\\\\implies P(X\geq 35)=12.3 \%`