Question

Suppose it is known that 40% of all college students work full time. Define a success as "a student works full time". (a) If we randomly select 12 college students, what is the probability that exactly 3 of the 12 students work full time? (show 5 decimal places) (b) If we randomly select 12 college students, what is the probability that at least 3 of the 12 work full time? (show 5 decimal places) (c) In questions (a) and (b) above, what does the number 12 represent? X 1-p n p k (d) A failure can be defined as: A student works part time A student does volunteer work A student does not work full time A student works full time A student does not have a job

Answer 1

a)

Here, n = 12, p = 0.4, (1 - p) = 0.6 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 3)
P(X = 3) = 12C3 * 0.4^3 * 0.6^9
P(X = 3) = 0.14189

b)

Here, n = 12, p = 0.4, (1 - p) = 0.6 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 3).
P(X >= 3) = (12C3 * 0.4^3 * 0.6^9) + (12C4 * 0.4^4 * 0.6^8) + (12C5 * 0.4^5 * 0.6^7) + (12C6 * 0.4^6 * 0.6^6) + (12C7 * 0.4^7 * 0.6^5) + (12C8 * 0.4^8 * 0.6^4) + (12C9 * 0.4^9 * 0.6^3) + (12C10 * 0.4^10 * 0.6^2)
P(X >= 3) = 0.14189 + 0.21284 + 0.22703 + 0.17658 + 0.1009 + 0.04204 + 0.01246 + 0.00249
P(X >= 3) = 0.91623

c)

the number 12 represent = x

d)

A student does not work full time