Question

1. the overall shape of this distribution is

a. roughly symmetric
b. uniform
c. skewed to the right
d. skewed to the left

1. the mean of this distribution

a. is less than the median
b. is greater than the median
c. is the same as the median
d. cannot be determined

1. select all the functions that would be considered exponential decay.

a $y = 2(0.7)^x$
b $y = 0.7(2)^x$
c $y = 0.9(3)^x$
d $y = 3(0.9)^x$

1. the test scores of the students in four classes are summarized below. answer the questions about them.

class a: the mean score is 114 and the range of scores is 23.
class b: the mean score is 110 and the range of scores is 31.
class c: the mean score is 105 and the range of scores is 28.
class d: the mean score is 107 and the range of scores is 32.
(a) based on the information above, which class’s scores have the most variability?
class a class b class c class d
(b) based on the information above, which class has the highest scores on average?
class a class b class c class d

Explanation:

Question 6

Step1: Analyze the histogram shape

The histogram's bars: left side has shorter bars, right side also has shorter bars, middle is taller. So it's roughly symmetric (not uniform, not skewed left/right as tails on both sides are similar in length).

Step2: Eliminate other options

• Uniform: bars would be similar height, not here.
• Skewed right: right tail longer, not here.
• Skewed left: left tail longer, not here.

Step1: Recall symmetric distribution property

In a roughly symmetric distribution (from Q6), the mean and median are approximately equal.

Step2: Evaluate options

Since distribution is symmetric, mean = median.

Step1: Recall exponential decay formula

Exponential decay has form \( y = ab^x \) where \( 0 < b < 1 \) (base between 0 and 1, so as \( x \) increases, \( y \) decreases).

Step2: Check each option

• A: \( b = 0.7 \) (0 < 0.7 < 1) → decay.
• B: \( b = 2 \) (>1) → growth.
• C: \( b = 3 \) (>1) → growth.
• D: \( b = 0.9 \) (0 < 0.9 < 1) → decay.

Answer:

A. roughly symmetric

Question 7