For each person, there are only two possible outcomes. Either they are afraid of being alone at night, or they are not. The probability of a person being afraid of being alone at night is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5% of Americans are afraid of being alone in a house at night.

This means that $p = 0.05$

If a random sample of 20 Americans is selected, what is the probability that exactly 3 people in the sample are afraid of being alone at night.

This is P(X = 3) when n = 20. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596$

5.96% probability that exactly 3 people in the sample are afraid of being alone at night.

5 0

3 years ago

Please help with explanation and pleasedo let me know about the method ( 9a,b 10a)

worty [1.4K]

Answer:

Hope this helps

Step-by-step explanation:

Crossproduct is explained. You can use it to get all the values as well as being able to convert into other currencies.

6 0

3 years ago

Please help!!!!!<br><br>Key features of Graphs

krok68 [10]

The graph is **increasing on the interval (-2, 1)**because the graph has a positive slope from x=-2 to x=1. It’s **decreasing at the intervals (-infinity, -2) and (1, infinity)**because the graph has a negative slope between the x values -infinity to -2 and is also decreasing between the x values of 1 and infinity.

6 0

3 years ago