Respuesta :
Using the normal approximation to the binomial distribution, it is found since np = 0.5 < 10, we cannot find the probability.
Normal Probability Distribution
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex], as long as [tex]np \geq 10, n(1 - p) \geq 10[/tex].
In this problem, we have that:
- Only 1% of the population has this blood type, hence p = 0.01.
- A random sample of 50 people is selected, hence n = 50.
Then:
np = 50 x 0.01 = 0.5 < 10.
Thus we cannot find the probability.
More can be learned about the normal approximation to the binomial distribution at https://brainly.com/question/14424710
