Suppose a set of test scores is appproximately bell-shaped, with a mean of 68 and a range of 54. (a) The minimum test score is approximately , and the maximum test score is approximately . (b) The standard deviation of the test scores is approximately g

a.) Minimum test score = 41

    Maximum test score = 95

b.)An approximate value of the standard deviation is 9.

Step-by-step explanation:

The given set of test scores is approximately bell shaped.

The mean of the test scores, = 68

The range of the data set = 54.

a.) i.) Minimum test score  =

   ii.) The maximum test score =

b.) From the 68-95-99.7 rule, also known as the Empirical rule, tell us that an approximation of the range is 3 standard deviations either way from the mean. So from this rule we can say that the minimum can also be found from and the maximum can also be approximated as .

From the above we can say that the range can be written as

∴  

∴    

Therefore an approximate value of the standard deviation is 9.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)