Question 1199365: Hello! Good morning!
I'm doing some binomial distribution problems and I got stuck in this one, I managed to solve a, b and c but I don't know how to solve d.
66% of all students at a college still need to take another math class. If 34 students are randomly selected, find the probability that
a. Exactly 20 of them need to take another math class.
0.09445
b. At most 21 of them need to take another math class.
0.36062
c. At least 22 of them need to take another math class.
0.63938
d. Between 22 and 28 (including 22 and 28) of them need to take another math class.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
Hello! Good morning!
I'm doing some binomial distribution problems and I got stuck in this one,
I managed to solve a, b and c but I don't know how to solve d.
66% of all students at a college still need to take another math class.
If 34 students are randomly selected, find the probability that
a. Exactly 20 of them need to take another math class.
0.09445
b. At most 21 of them need to take another math class.
0.36062
c. At least 22 of them need to take another math class.
0.63938
d. Between 22 and 28 (including 22 and 28) of them need to take another math class.
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So, you just know that it is a typical Binomial distribution problem.
The number of trials is n= 34; the number of successful trials is "k",
different in different questions;
The probability of success of each individual trial is p= 0.66.
You may use an appropriate online (free of charge) calculator at this web-site
https://stattrek.com/online-calculator/binomial.aspx
It provides nice instructions and a convenient input and output for all relevant options/cases.
(a) P = P(n=34; k=20; p=0.66) = 0.09445. You just know it . . .
(b) P = P(n=34; k<=21; p=0.66) = 0.36062. You just know it . . .
(c) P = P(n=34; k>=22; p=0.66) = 0.63938. You just know it . . .
(d) P = P(n=34; k<=28; p=0.66) - P(n=34; k<=21; p=0.66) <<<---=== you calculate the needed probability
as this DIFFERENCE of standard cumulative probabilities
using the standard functions
= use the referenced calculator = 0.9895 - 0.36062 = 0.6289 (rounded). ANSWER
Solved and explained.
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The major lesson to learn from my post is that the probability (d) is the difference of the appropriate
 probabilities, which you can calculate using the standard functions.
Which tool you will use - online calculator or your hand calculator - is just the secondary matter,
while the first row matter is to know WHAT to do.
Happy learning ( ! )
//////////////////
At this site, there are several lessons where many similar problems were solved and presented in all details
- Simple and simplest probability problems on Binomial distribution
- Typical binomial distribution probability problems
- Solving problems on Binomial distribution with Technology (using online solver)
Look into these lessons.
After reading/learning from these lessons, you will be able to solve such problems on your own, which is your
PRIMARY MAJOR GOAL visiting this forum (I believe).
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! not sure how you did it, but these are the results i got using excel to perform the calculations.
the probability of between 22 and 28 is simply the sum of p(22) through p(28).
you should get 0.628878118 as shown in the excel file.
your other proabilities are good.
let me know if this works for you.
theo
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