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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

Answer :

fichoh

Answer:

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

About 95% of the scores should fall between 442 and 606.

Calculation of the range:

Since the mean is 524 and the standard deviation is 41

So, here the range should be

[tex]= \mu \pm 2\sigma\\\\= 524 \pm (2 \times 41)\\\\[/tex]

= (442,606)

Like for the answer 442, the calculation is done below:

[tex]= 524 - (2\times 41)\\\\= 524 - 82\\\\= 442[/tex]

Now for the answer 606, it should be

[tex]= 524 + (2\times 41)\\\\= 524 + 82\\\\= 606[/tex]

Learn more about the score here: https://brainly.com/question/1863752

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