The average score of a statistics class was 71 with a standard deviation of 10

The average score of a statistics class was 71 with a standard deviation of 10.

1. What is the z score of a student with a grade of 68? (2.5 pts)

2. What is the z score of a student with a grade of 80? (2.5 pts)

Using the same data in #1 answer the following:

1. Approximately 68% (one standard deviation) of the scores are between ________ and _________ (2.5 pts)

2. Approximately 95% (two standard deviation) of the scores are between _________ and _________ (2.5 pts)

Most values of a standard normal distribution are between __________. (3 pts)

1. -3 and 3

2. 0 and 1

3. 0 and 3

4. 1 and 3

(a) If the standard deviation of a data set is 1.3, what is the variance? (2.5 pts)
(b) If the variance is 36, what is the standard deviation? (2.5 pts)

Let X have a normal distribution with mean µ = 20 and standard deviation σ = 4. 
Determine the area in the normal curve for which:

1. P(X > 28) (2.5 pts)

2. P(X < 12) (2.5 pts)

3. P(16 < X < 24) (2.5 pts)

The IQ scores of students listed below are from a SAMPLE of MATH 300 class.

1. What is the mean IQ score? Round to the nearest whole number. (2.5 pts)

2. Compute the IQ scores within plus/minus one standard deviation? Two answers. Round to the nearest whole numbers. (2.5 pts)

3. Compute the IQ scores within plus/minus two standard deviation? Two answers. (2.5 pts)

Let X have a normal distribution with µ= 10 and standard deviation σ= 2. Transform X to the standard normal form Z and match the following probability statements:
a) P(X>14)                                          1) P(Z<-1)
b) P(X<8)                                            2) P(-2 < Z < 2)
c) P(6 < X < 14)                                  3) P(Z > 2)
a) is matched to ___________ (2.5 pts)
b) is matched to ___________ (2.5 pts)
c) is matched to ___________ (2.5 pts)

Let X have a normal distribution with mean µ= 30 and standard deviation σ= 10. Calculate P(X>40). Round to two decimal places. (4 pts)

For a standard normal variable Z, compute P(Z<1.5). Round your answer to two decimal places. (3 pts)

A larger standard deviation of a normal distribution indicates that the distribution becomes (2.5 pts)

1. narrower and more peaked

2. flatter and wider

3. more skewed to the right

4. more skewed to the left