Question

What is the probability that out of 60 lambs born on BaaBaa Farm, at least 31

will be male? Assume that males and females are equally probable, and
round your answer to the nearest tenth of a percent.

Answer 1

44.9% (nearest tenth)

Explanation:

We can solve this by using a binomial distribution since:

• Fixed number of trials (60)
• Two possible results: male and female
• All trials are independent
• Constant probability of success (0.5)
• X is the total number of males in the trials

X ~ B(n, p) ⇒ X ~ B(60, 0.5)

P(X ≥ 31) = 1 - P(X ≤ 30)

= 1 - 0.5512890796

= 0.4487109204...

= 44.9% (nearest tenth)

Answer 2

44.9%

Explanation:

The probability 31 or more will be male is the same as the probability that 29 or fewer will be female. A suitable calculator shows that to be ...

p(m≥31) ≈ 0.449 = 44.9%

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Numerous apps and spreadsheets can figure values from the binomial probability distribution.