Respuesta :
Answer:
(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:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]x\ is \ the\ number\ evaluated\\\mu\ is\ the\ mean\\\sigma\ is \ the \standard\ deviation[/tex]
(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
The percentage between [tex]\pm[/tex]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 [tex]\pm[/tex]1 standard deviation from the mean the percentage in that band correspond to the 68% of the values.
If [tex]\pm[/tex]2 standard deviation from the mean the percentage in that band correspond to the 95% of the values.
If [tex]\pm[/tex]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:
[tex]z = \frac{x-\mu}{\sigma}[/tex]
n = evaluate numbers.
[tex]\mu[/tex] = mean and [tex]\sigma[/tex] = deviation.
- The percentage of standardized test scores is between 190 and 850 lower z = [tex]\frac{190-520}{110}[/tex] = -3
And upper z = [tex]\frac{850-520}{110}[/tex] = 3
This means percentage between [tex]\pm[/tex]3 standard deviation, exactly 99.7%
- The percentage of standardized test scores is less than 190 or greater than 850.
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%
- The percentage of standardized test scores is greater than 740
z of 740 = [tex]\frac{740-520}{110}[/tex] = 2
The percentage between [tex]\pm[/tex]2 is 95%, the percentage greater than 2 and that is [tex]\frac{100-95}{2}[/tex] = 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 .
For the more information about Probability click the link given below.
https://brainly.com/question/23044118
