The national average for mathematics on a standardized test in 2011 was 524. Suppose that the distribution of scores was approximately bell-shaped and that the standard deviation was

approximately 41. Round your answers to one decimal place as needed.

Part 1 out of 2

Within what boundaries would you expect 95% of the scores to fall?

About 95% of the scores should fall between

and

As

Step-by-step explanation:

Given the following :

Mean score in test (m) = 524

Standard deviation (sd) = 41

Within what boundaries would you expect 95% of the scores to fall?

Using the Zscore formula :

Zscore = (score - mean) / standard deviation

For a normal distribution, 95% score will have a Zscore value of (-1.96 < Z < 1.96)

For Zscore = - 1.96

-1.96 = (X - 524) / 41

41 * - 1.96 = X - 524

-80.36 = X - 524

X = - 80.36+ 524

= 443.46

For Zscore = 1.96

1.96 = (X - 524) / 41

41 * 1.96 = X - 524

80.36 = X - 524

X = 80.36+ 524

= 604.36

step-by-step explanation:

answerthe vertex form

step-by-step explanation: