Sahil Khan

A small college has 800 students, 10 percent of which are left-handed. Suppose we randomly select 8 students, because SRS = 8, and assume L = 3.

Also, assume we have to find the probability that exactly 3 out of the 8 students are left-handed, or the probability that L=3.

We use the binomial distribution for calculating this

^{n}C_{r} \cdot p^{r} (1-p)^{n-r}

p is the probability of successes which is 10% or 0.1, n = 8, r = 3. Plugging these in we get


= 56 (0.001)(0.9)^{5}


So, the probability of getting 3 lefthanded students is 0.033.

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Sangeetha Pulapaka

I may be able to help you if you complete the question. Do you want to find the probability of the left handed students in the sample here or the mean and the standard deviation?

Here is a similar discussion based on the first few words in your statement which may help

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Binomial probability example (video) | Khan Academy

We can use the binomial distribution to find the probability of getting a certain ... Binomial random variables ... Binomial mean and standard deviation formulas ... It may not be exact because this is experimental data, but it should be close. ... AP® is a registered trademark of the College Board, which has not reviewed this  ...

For more information, see Binomial probability example (video) | Khan Academy