27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 39 college students are randomly selected, find the probability that a. Exactly 9 of them major in STEM.  b. At most 10 of them major in STEM.  c. At least 11 of them major in STEM.

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27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 39 college students are randomly selected, find the probability that

a. Exactly 9 of them major in STEM. 
b. At most 10 of them major in STEM. 
c. At least 11 of them major in STEM. 
d. Between 6 and 13 (including 6 and 13) of them major in STEM. 

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Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a time so we are answering the first three as you have not mentioned which of these you are looking for. Please re-submit the question separately for the remaining sub-parts.

From the given information,

Consider, X be the random variable that shows the major in STEM which follows binomial distribution.

That is, 

X~binn=39,p=0.27fx=39x0.27x×1-0.2739-x,x=0,1,2,,,,,,,,

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