Question

Answer the following questions and round your answers to 2 decimal places. 31% of all college students major in STEM (Science, Technology, Engineering, and Math). If 36 students are randomly selected, find the probability that

Answer 1

Answer:

$\mathbf{P(X =11 ) \simeq 0.1429}$

Step-by-step explanation:

The objective of this question is to find the probability that:

Exactly 11 of them major in STEM

So, Let assume X to be the random variable that follows a binomial distribution:

Then $X \simeq Bin ( 36, 0.31)$

The probability that exactly 11 of them major in STEM can be computed as:

$P(X =11 ) = ^{36} C_{11} (0.31)^{11} (1-0.31) ^{36-11}$

$P(X =11 ) = \dfrac{36!}{11!(36-11)!} \times (0.31)^{11} \times (0.69) ^{25}$

$P(X =11 ) = \dfrac{36!}{11!(36-11)!} \times (0.31)^{11} \times (0.69) ^{25}$

$P(X =11 ) =600805296 \times (0.31)^{11} \times (0.69) ^{25}$

$\mathbf{P(X =11 ) \simeq 0.1429}$

Thus; the probability that exactly 11 of them major in STEM is 0.1429