1. A variable X has a distribution which is described by the density curve shown below:

What proportion of values of X fall between 1 and 6? (A) 0.550 (B) 0.575 (C) 0.600 (D) 0.625 (E) 0.650

2. Which of the following statements about a normal distribution is true? (A) The value of µ must always be positive. (B) The value of σ must always be positive. (C) The shape of a normal distribution depends on the value of µ. (D) The possible values of a standard normal variable range from −3.49 to 3.49. (E) The area under a normal curve depends on the value of σ.

3. A variable X follows a uniform distribution, as shown below:

The distribution of X has an interquartile range equal to 4 (since the middle 50% of the data are contained between the values 2 and 6). Consider the variables with the distributions shown below (assume that the heights of the curves are such that they are both valid density curves):

The interquartile range of density curve (I) is of density curve (II) is . (A) (I) less than 4, (II) greater than 4 (B) (I) greater than 4, (II) less than 4 (C) (I) equal to 4, (II) equal to 4 (D) (I) less than 4, (II) less than 4 (E) (I) greater than 4, (II) greater than 4

and the interquartile range

4. A variable X has a uniform distribution on the interval from 2 to 6. The P (4.2 < X < 5.7) is equal to: (A) 0.375 (B) 0.475 (C) 0.575 (D) 0.675 (E) 0.775

5. A variable Z has a standard normal distribution. What is the value b such that P (−0.37 ≤ Z ≤ b) = 0.5749? (A) 2.02 (B) 1.48 (C) 0.97 (D) 0.63 (E) 1.72

6. What is the P (Z > −0.75)? (A) 0.2266 (B) 0.7734 (C) 0.0401 (D) 0.9599 (E) 0.4289

7. A variable X has a normal distribution with mean 100. It is known that about 47.5% of the values of X fall between 85 and 100. What is the approximate value of the standard deviation σ? (A) 5 (B) 7.5 (C) 12.5 (D) 15 (E) 30

8. Suppose that the variable Z follows a standard normal distribution. If P (−b < Z < b) = 0.92, then b...

(1)