Question

Suppose that 15% of the U.S. population has some type of learning disorder

a) Consider a simple random sample of size 300. Check that the conditions for the sample proportion to be approximately normal are met. What is the probability that the proportion of people in the sample with a learning disorder is at least 0.12?

(b) How would you compute the probability that at least 36 members of a simple random sample of size 300 chosen from the U.S. population will have a learning disorder? Explain what you would do, but do not actually compute it.

(c) It turns out the probability that at least 36 members of a simple random sample of size 300 chosen from the U.S. population will have a learning disorder is approximately 0.9412. Compare this answer in part a. Would you expect them to be similar? Why or why not?

Answer 1

the proportion of U.S. population that has some type of learning disorder: p = 0.15

a) condition for the sample to meet to be approximately normal

and

n= 300

the following condition is met

the probability that the proportion of people in the sample with a learning disorder is at least 0.12 is

b) we will find the mean and standard deviation for normal approximation

Then you can convert 36 to standard Z score and compute the probability.

c) normal distribution is a continuous distribution you have to add continuity correction first. That is why the probability is slightly varying in a and c

if you do the continuity correction

the probability that at least 36 members of a simple random sample of size 300 chosen from the U.S. population will have a learning disorder is

which is approximately same as 0.9412