Question

1. in a normal distribution, which of the following statements is true about the area that falls between one standard deviation above and one standard deviation below the mean? (2013 ap psychology exam)

a. it contains the bottom 50% of the distribution
b. it contains the middle 50% of the distribution
c. it contains the bottom 68% of the distribution
d. it contains the middle 68% of the distribution
e. it is the same as the square of the average deviation

1. on a test, the mean score for a class of 100 students is 80 and the standard deviation of the scores is 10. the professor who gave the test then realizes that she made a scoring error, which she corrects by adding 5 points to each student’s score. the standard deviation of students’ new scores is (2013 ap psychology exam)

a. 5
b. 10
c. 10.5
d. 15
e. 85

1. tamar scores 145 on an iq test with a mean of 100 and a standard deviation of 15. what is her z - score? (barron’s ap psychology, 4e.)

a. -3
b. -1.5
c. +0.67
d. 1.5
e. +3

1. sandy scores a perfect 100 on a test that everyone else fails. if we were to graph this distribution, it would be (barron’s ap psychology, 4e.)

a. symmetrical
b. normal
c. positively skewed
d. negatively skewed
e. a straight line

1. which of the following is true of the frequency distributions shown in the graphs below? (2012 ap psychology exam)

a. distribution a has more variation than distributions b or c.
b. distribution b has more variation than distributions a or c
c. distribution b and distribution c have the same variation.
d. the standard deviation of distribution a is infinite.
e. the standard deviation of distribution b is zero.

Explanation:

1. In a normal distribution, approximately 68% of the data falls within one - standard deviation of the mean, which is the middle 68% of the distribution.
2. Adding a constant to each data - point in a set does not change the standard deviation. The spread of the data relative to each other remains the same.
3. The z - score is calculated using the formula $z=\frac{x-\mu}{\sigma}$, where $x = 145$, $\mu=100$, and $\sigma = 15$. So $z=\frac{145 - 100}{15}=\frac{45}{15}=3$.
4. When one value is much larger than the rest (Sandy's perfect score while others fail), the distribution is positively skewed.
5. A distribution with all data points having the same value has a standard deviation of zero. If distribution B has all identical values, its standard deviation is zero.

Answer:

1. D. It contains the middle 68% of the distribution
2. B. 10
3. E. +3
4. C. Positively skewed
5. E. The standard deviation of distribution B is zero.