Go tohttps://rconnect.byu.edu/Stat121App/ On the left panel, select "Normal Probability Calculator".

Suppose that the average score for a quiz is 84 with a standard deviation of 5. Assume the distribution is normal.

1. What is the probability that a randomly selected student's score is less than 80?

A.0.2119

B.0.5763

C.0.7881

D.0.8

2. What is the probability that a randomly selected student's score is greater than 85?

A.0.1587

B.0.2

C.0.4207

D.0.5793

The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain postbaccalaureate students to promote access to postsecondary education. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600. Assume that the standard deviation,, in Pell grant awards was $500, and that the distribution is right skewed.

3.Suppose we take random samples of size 75. What will the mean of the sampling distribution of x be?

A.$500

B.$300.23

C.$2,600

D.$5,200

1. For samples of size 75, what will the standard deviation of the sampling distribution of x be?

A.$57.74

B.$27.21

C.$6.67

D.$500

5.If we take samples of size 200 rather than 75, what will happen to the mean of the sampling distribution of x?

A.The mean will decrease

B.The mean will stay exactly the same

C.The mean will be almost the same

D.The mean will increase

6. If we take samples of size 200 rather than 75, what will happen to the standard deviation of the sampling distribution of x?

A.The standard deviation will decrease

B.The standard deviation will stay the same

C.The standard deviation will increase

7.If we take random samples of size 75 from this population, what will the shape of the sampling distribution of x be?

A.Approximately Normal

B.Left-skewed

C.Right-skewed

D.Not enough information to tell

The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain postbaccalaureate students to promote access to postsecondary education. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600. Assume that the standard deviation,, in Pell grant awards was $500, and that the distribution is right skewed.

8.What is the probability that a randomly selected grant award will exceed (is greater than) $2700?

A.0.0173

B.0.5675

C.0.9582

D.0.0418

E.Cannot be calculated from the given information

9.Suppose we have an extremely left-skewed population with a mean of 45 and a standard deviation of 7. Can we compute the probability that x is less than 32 for a random sample of size 15?

A.Yes, because we know the mean and standard deviation of the sampling distribution of x.

B.Yes, because the sampling distribution of x-bar is Normally distributed.

C.No, because the population is not Normally distributed and we cannot apply the Central Limit Theorem.

10.Refer to the situation in Question 7. Suppose we took samples of size 45. What will be the shape of the sampling distribution of x?

A.Approximately Normal

B.Slightly right skewed

C.Slightly left skewed

D.Normal

Go tohttps://rconnect.byu.edu/Stat121App/ On the left panel, select "Sampling Distribution of X-bar".

11. Assume the population is normally distributed. What happens to the shape of the sample as the sample size increases?

A.It looks less normal.

B.It looks more and more like the population distribution.

C.It looks more and more like the sample distribution.

D.Sample size does not impact the shape of the sampling distribution of x-bar.

1. If all possible samples of size 20 are taken instead of size 100, how would this change the mean and standard deviation of the sampling distribution of x?

A.The mean would decrease and the standard deviation would decrease.

B.The mean would decrease and the standard deviation would increase.

C.The mean would increase and the standard deviation would decrease.

D.The mean would increase and the standard deviation would increase.

E.The mean would stay the same and the standard deviation would decrease.

F.The mean would stay the same and the standard deviation would increase.