Question

Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that at most 4 students have taken chemistry? Round the answer to the nearest thousandth.
a. 0.008
b. 0.438
c. 0.562
d. 0.665

Answer 1

Answer:

Option b

Step-by-step explanation:

Given that Mrs. Gomes found that 40% of students at her high school take chemistry

since each student is independent of the other, we can say

X no of students who take chemistry is binomial with p = constant proba = 0.40

n = no of trials = no of students surveyed =12

Required probability = prob atmost 4 students take chemistry

=$P(X\leq 4)\\=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)\\=\Sigma _0^4 12Cr (0.4)^r (0.6)^{12-r}$

Substituting we get the cumulative probability

as

0.4382

round off to 0.438

Option b is correct answer