Question

A teacher decided to bring a jar of 530 pieces of small candy to his 100-student classroom so students could practice estimation. The students were told that whoever had the closest guess would win the candy. Suppose we took a random sample of one third of the students and calculated the sample mean of their guesses. The distribution of individual guesses had a mean of 400 pieces of candy and a standard deviation of 3,000 pieces of candy (the students had a lot of trouble guessing the count).

Is it appropriate to use a normal distribution to approximate the sampling distribution of the sample mean?
Hint: check your assumptions and consider, if applicable, what the distribution would look like.
a. Yes, because the population distribution is normally distributed, and we have a random sample.
b. Yes, because the sample size is at least 30, and we have a random sample.
c. Yes, because np and nq are both at least 10, and we have a random sample.
d. No, because we don’t have a random sample.
e. No, because the sample size isn’t at least 30 and the population isn’t normally distributed.
f. No, because np and nq aren’t both greater than 10.
g. No, because we would need a larger sample size before the sampling distribution would be reasonably normally distributed.

Answer 1

B

Explanation:

Yes, because the sample size is at least 30, and we have a random sample.

We have our sample size to be 33% of the student = 33 student (approx)

- According to conditions of normality which states that the sample size collected from a normally distributed population with 100 students should have a sample size of at-least 30 students.

- This condition approximates that the sample collected is also random and and follows a normal distribution like the population ( i.e total number of students = 100 ) itself.

- However, the spread of the data sigma = 3,000 is very large but it does not invalidates the condition of normally distributed sample, it only means that values are spread wide about the mean = 400.