a. Exactly 11 of them major in STEM.  b. At most 16 of them major in STEM.  c. At least 15 of them major in STEM.  d. Between 7 and 11 (including 7 and 11) of them major in STEM.

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26% of all college students major in STEM (Science, Technology, Engineering, and Math). If 49 college students are randomly selected, find the probability that

a. Exactly 11 of them major in STEM. 
b. At most 16 of them major in STEM. 
c. At least 15 of them major in STEM. 
d. Between 7 and 11 (including 7 and 11) of them major in STEM.

Expert Solution
Step 1

a.

The Binomial probability distribution is:

PX=x=nxpx1-pn-x

In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.

Let X be the major in STEM which follows binomial distribution with sample size 49, and probability of success 0.26.

The probability that exactly 11 of them major in STEM is,

PX=11=49110.26111-0.2649-11=0.1148

Thus, the probability that exactly 11 of them major in STEM is 0.1148.

 

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