Acertain standardized test's math scores have a bell-shaped distribution with a mean of 520 and a standard deviation of 110. complete parts (a) through (c).

(a) what percentage of standardized test scores is between 190 and 850? (round to one decimal place as needed.)

(b) what percentage of standardized test scores is less than 190 or greater than 850? (round to one decimal place as needed.)

(c) what percentage of standardized test scores is greater than 740? (round to one decimal place as needed.)

The percentage between 3 standard deviation, exactly 99.7%.

The percentage between is 99.7%, the percentage less than -3 standard deviation or greater than +3 standard deviation is 100 - 99.7 = 0.3%.

standard deviation and 2.5% is greater than 2 standard deviation, and the percentage greater than.

Given that,

A certain standardized test's math scores have a bell-shaped distribution with a mean of 520 and a standard deviation of 110.

We have to complete the following statements.

According to the question,

If 1 standard deviation from the mean the percentage in that band correspond to the 68% of the values.

If 2 standard deviation from the mean the percentage in that band correspond to the 95% of the values.

If 3 standard deviation from the mean the percentage in that band correspond to the 99.7% of the values.

The formula to calculate z-score is:

n = evaluate numbers.

= mean and = deviation.

And upper z = = 3

This means percentage between 3 standard deviation, exactly 99.7%

Since the percentage between is 99.7%, the percentage less than -3 standard deviation or greater than +3 standard deviation is 100 - 99.7 = 0.3%

z of 740 = = 2

The percentage between 2 is 95%,  the percentage greater than 2 and that is = 2.5%.

You have to divide by 2 because 2.5% is less than -2 , standard deviation and 2.5% is greater than 2 standard deviation, and the percentage greater than .

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(a) 99.7%

(b) 0.3%

(c) 2.5%

Step-by-step explanation:

This problem doesnt require a z-table as long as you know the basic rule of 68, 95 and 99.7.

If you are +-1 standard deviation from the mean the percentage in that band correspond to the 68% of the values.

If you are +-2 standard deviation from the mean the percentage in that band correspond to the 95% of the values.

If you are +-3 standard deviation from the mean the percentage in that band correspond to the 99.7% of the values.

The formula to calculate z-score is:

(a)

lower z = (190 - 520)/110 = -3

upper z = (850 - 520)/110 = 3

This mean that you are looking for a percentage between +-3 standard deviation, exactly 99.7%

(b)

Since the percentage between is 99.7%, the percentage less than -3 standard deviation or greater than +3 standard deviation is 100 - 99.7 = 0.3%

(c)

z of 740 = (740 - 520)/110 = 2

The percentage between +-2 is 95%, you are interested in the percentage greater than 2 and that is (100 - 95)/2 = 2.5%. You have to divide by 2 because 2.5% is less than -2 standard deviation and 2.5% is greater than 2 standard deviation, and you are only interested in the percetange greater than that