Statistics help. How to find probability?

[cruisx]

hey so i am trying to solve the following question but i have no idea how to solve it. I am confused by the %'sConsider a similar study done that shows that 96 % of those born in Canada can swim but only 83 % of new Canadians can swim. In a random group of 11 new Canadians, find the probability that at least 10 can swim.

The answer is 0.418933112054558

How is this answer obtained?
Now for at least, do i do p(10) + p(11), do i use a binomial formula or another one. I tried to do the mew = npq but that is not correct.

 

[mathman]

Use the binomial formula.

 

[cruisx]

THis one?

nCr p^r q^n-r

so

11C10 (0.83)^10 * (0.17)^1. Well its late, ill come back in the morning and try it again.

 

[HallsofIvy]

At least 10 means 10 or 11.

It is, as you said, p(10)+ p(11)=
$$_{11}C_{10}(.83)^{10}(.17)+ _{11}C_{11}(.83)^{11}= 11(.83)^{10}(.17)+ (.83)^{11}$$.

 

[CellCoree]

To find the probability in this scenario, you would use the binomial probability formula. This formula is used when there are two possible outcomes (in this case, being able to swim or not being able to swim) and the probability of each outcome is known (96% and 83%).

First, we need to determine the values for n, p, and q:
- n = 11 (since we are considering a random group of 11 new Canadians)
- p = 0.83 (probability of a new Canadian being able to swim)
- q = 0.17 (probability of a new Canadian not being able to swim)

Next, we can use the formula P(x ≥ k) = 1 - P(x < k-1) to find the probability of at least 10 new Canadians being able to swim. This translates to:
P(x ≥ 10) = 1 - P(x < 9)

To calculate P(x < 9), we can use the binomial probability formula:
P(x < 9) = nCr * p^x * q^(n-x)
where nCr is the combination formula (n choose r) and x is the number of successes we are considering.

Plugging in the values, we get:
P(x < 9) = 55 * 0.83^9 * 0.17^2 = 0.418933112054558

Finally, we can find the probability of at least 10 new Canadians being able to swim:
P(x ≥ 10) = 1 - 0.418933112054558 = 0.581066887945442 or approximately 58.11%.

I hope this helps you understand how to find probability using the binomial formula in this scenario. If you are still confused, I suggest seeking help from a tutor or reaching out to your teacher for further clarification.