Question

In the U.S., 51% of all births are boys, and 49% are girls.
Use the binomial model to find the probability that 6 out of
10 births at a local hospital are boys.
P (x) = [ ]
n!
x!(n−x)!
p
xq
n−x
a. 17%
b. 21%
c. 49%
d. 51%

Answer 1

To find the probability using the binomial model, we need to plug in the values into the formula:

P(x) = (n! / (x!(n-x)!)) * p^x * q^(n-x)

Here, n = 10 (the number of births), x = 6 (the number of boys), p = 0.51 (the probability of a boy), and q = 0.49 (the probability of a girl).

P(x) = (10! / (6!(10-6)!)) * (0.51^6) * (0.49^(10-6))

P(x) = (10! / (6!4!)) * (0.51^6) * (0.49^4)

P(x) = (10 * 9 * 8 * 7 * 6! / (6!4!)) * (0.51^6) * (0.49^4)

P(x) = (10 * 9 * 8 * 7) * (0.51^6) * (0.49^4)

P(x) = 1680 * (0.51^6) * (0.49^4)

Using a calculator, we find that P(x) is approximately 0.215, which is 21.5%. Therefore, the correct answer is b. 21%.