According to a recent reporting on a standardized test, the average ERW (English, Reading, Writing) score for students in a particular state was 521. Assume the scores are Normally distributed with a standard deviation of 96.Answer parts a through c below including an appropriately labeled and shaded Normal curve for each part.a. What percentage of the ERW test takers from this state scored 500 or less? Select the correct graph below.OA.В.500500233521809233521809D.500500233521809233521809The percentage that scored 500 or less is%.(Round to one decimal place as needed.)b. What percentage of the ERW test takers from this state scored between 500 and 644? Select the correct graph below.OA.В.500500,644644233521809233521809DensityDensityDensityDensityDensityDensity According to a recent reporting on a standardized test, the average ERW (English, Reading, Writing) score for students in a particular state was 521. Assume the scores are Normally distributed with a standard deviation of 96.Answer parts a through c below including an appropriately labeled and shaded Normal curve for each part.500500644644233521809233521809The percentage that scored between 500 and 644 is%.(Round to one decimal place as needed.)c. What ERW score would correspond with the 40th percentile in this state? Select the correct graph below.O A.QВ.40%|40%233521809233521809D.Q60%60%233521809233521809A score ofcorresponds with the 40th percentile in this state.(Round to the nearest integer as needed.)C.DensityDensityDensityB.DensityDensityDensity

a. The random variable X is defined as the ERW score for students in a particular state which…

According to a recent reporting on a standardized test, the average ERW (English, Reading, Writing) score for students in a particular state was 521. Assume the scores are Normally distributed with a standard deviation of 96. Answer parts a through c below including an appropriately labeled and shaded Normal curve for each part.

According to a recent reporting on a standardized test, the average ERW (English, Reading, Writing) score for students in a particular state was 521. Assume the scores are Normally distributed with a standard deviation of 96. Answer parts a through c below including an appropriately labeled and shaded Normal curve for each part.

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

According to a recent reporting on a standardized test, the average ERW (English, Reading, Writing) score for students in a particular state was 521. Assume the scores are Normally distributed with a standard deviation of 96.
Answer parts a through c below including an appropriately labeled and shaded Normal curve for each part.
a. What percentage of the ERW test takers from this state scored 500 or less? Select the correct graph below.
OA.
В.
500
500
233
521
809
233
521
809
D.
500
500
233
521
809
233
521
809
The percentage that scored 500 or less is
%.
(Round to one decimal place as needed.)
b. What percentage of the ERW test takers from this state scored between 500 and 644? Select the correct graph below.
OA.
В.
500
500,
644
644
233
521
809
233
521
809
Density
Density
Density
Density
Density
Density

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