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).

Yes, because the population distribution is normally distributed, and we have a random sample.

Step-by-step explanation:

If the population is skewed, then the sample mean won't be normal for when N is small.

If the population is normal, then the distribution of sample mean looks normal even if N = 2.

If the population is skewed, then the distribution of sample mean looks more and more normal when N gets larger.

Since we have use 33% of the student, then N is large enough to conclude that the student are bad at guessing

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8