Question

According to a recent study, what is the probability that 2 in every 5 women has been a victim of domestic abuse? This probability was obtained from a survey of 1,000 adult women. Suppose we randomly sample 10 women and find that 5 have been abused.

a. What is the probability of observing 5 or more abused women in a sample of 15 if the proportion p of women who are victims of domestic abuse is really p = 3/8 ?

Answer 1

To find the probability of observing 5 or more abused women in a sample of 15, we can use the binomial distribution formula. The formula for the probability mass function of the binomial distribution is P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where P(X = k) is the probability of observing k successes, C(n, k) is the number of combinations of n items taken k at a time, p is the probability of success (3/8 in this case), and n is the number of trials (15 in this case).

Step-by-step explanation:

To find the probability of observing 5 or more abused women in a sample of 15, we can use the binomial distribution formula. The formula for the probability mass function of the binomial distribution is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

where:

• P(X = k) is the probability of observing k successes
• C(n, k) is the number of combinations of n items taken k at a time
• p is the probability of success (3/8 in this case)
• n is the number of trials (15 in this case)

To find the probability of observing 5 or more abused women, we need to calculate the following probabilities:

1. P(X = 5)
2. P(X = 6)
3. P(X = 7)
4. P(X = 8)
5. P(X = 9)
6. P(X = 10)
7. P(X = 11)
8. P(X = 12)
9. P(X = 13)
10. P(X = 14)
11. P(X = 15)

We can then sum up these probabilities to get the probability of observing 5 or more abused women in a sample of 15.