Question

Math

Posted 4 months ago

```
A small college has 800 students, $10 \%$ of which are left-handed. Suppose they take an SRS of 8 students. Let $L=$ the number of left-handed students in the sample.
Which of the following would find $P(L=2)$ ?
Choose 1 answer:
(A) $\binom{800}{8}(0.10)^{2}(0.90)^{6}$
(B) $\binom{8}{2}(0.10)^{6}(0.90)^{2}$
(c) $\binom{8}{2}(0.10)^{2}(0.90)^{6}$
(D) $(0.10)^{6}(0.90)^{2}$
(E) $(0.10)^{2}(0.90)^{6}$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 2

Determine the values for $n$, $k$, and $p$: $n=8$ (sample size), $k=2$ (number of left-handed students), and $p=0.10$ (probability of being left-handed)

step 3

Apply the values to the binomial probability formula: $P(L=2) = \binom{8}{2}(0.10)^2(0.90)^{8-2}$

C

Key Concept

Binomial Probability Distribution

Explanation

The binomial probability distribution is used to calculate the probability of having a certain number of successes in a fixed number of independent trials, with a constant probability of success on each trial.

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