Probability and statistics

Solution 1:
Let X be random variable denotes the total number of eligible peoples. It is given that only 4% general population has trait.
Thus, p = 0.04
Here we need to find the probability that they need to interview 150 peoples before they found the 10th eligible volunteer. Here, negative binomial distribution is appropriate to use because in negative binomial we find the number of successes till a fixed value. Here, the success is before they found 10th eligible volunteer.
Thus, the probability is calculated as follows:
Solution 2:
Consider the given data set in the frequency distribution as follows:
The hypotheses are given as follows:
Null hypothesis: Data comes from Poisson distribution.
Alternative hypothesis: Data does not come from Poisson distribution.
The mean is calculated as follows:
Thus, the mean
Now we will calculate the expected frequency as follows:
First calculate the probability value for...