For each graduate, there are only two possible outcomes. Either they entered a profession closely related to their college major, or they did not. The probability of a graduate entering a profession closely related to their college major is independent of other graduates. This, coupled with the fact that they are chosen with replacement, means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

53% reported that they entered a profession closely related to their college major.

This means that $p = 0.53$

9 of those survey subjects are randomly selected

This means that $n = 9$

What is the probability that 3 of them entered a profession closely related to their college major?

This is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{9,3}.(0.53)^{3}.(0.47)^{6} = 0.1348$

0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.

6 0

2 years ago

Tyrell read 72 pages in 2 hours. At this rate, how many hours will it take him to read 285 pages?

juin [17]

It will take Tyrell about 4 hours.

4 0

2 years ago

The average height of a family of five is 150 cm. If the height of 4 family members is 153, 150, 151, and 152, find the height o

Lady bird [3.3K]

J can find the height of the fifth member on this way
S=150
S1=153
S2=150
S3=151
S4=152
S5=?
S= (s1+s2+s3+s4+s5)/5:
5*150= <span>153+150+151+152+S5
S5=5*150-606=750-606=144
Answer is 144 cm</span>

5 0

2 years ago