A). The following exercise refers to scores on standardized exams with results t

Question

A). The following exercise refers to scores on standardized exams with results that are normally distributed. Round your answer to one decimal place. Suppose you have a score that puts you 1.3 standard deviations below the mean. What is your percentile score?

B). The following exercise refers to scores on standardized exams with results that are normally distributed. Round your answer to one decimal place.
Suppose you have a score that puts you in the 60th percentile. What is your z-score?

C). A person's IQ (Intelligence Quotient) is supposed to be a measure of his or her "intelligence." The IQ test scores are normally distributed and are scaled to a mean of 100 and a standard deviation of 15.
If your IQ is 115, what is your percentile score? Round your answer to one decimal place.

D). In this exercise, we suppose that you had a score of 670 on the verbal section of the SAT Reasoning Test (see the SAT Verbal Scores table). Round your answers to one decimal place.

What is the z-score for this SAT score?

z =

What is your percentile score?

E). The heights of adult men in America are normally distributed, with a mean of 69.1 inches and standard deviation of 2.65 inches.

What percentage of adult males in America are over 6 feet 2 inches tall? Round your answer as percentages to the nearest whole number.
%

F). Suppose an exam had an average (mean) score of 70% and a standard deviation of 15%.

If the teacher curved grades using the bell curve as in the table above, what score would be necessary to receive an "A"? Round your answer a percentage to one decimal place.

To receive an "A" a score of % would be needed.

How about a "B"? Round your answers as percentages to one decimal place. (Enter your answers from smallest to largest.)

To receive a "B" a score between % and % would be needed.

How about a "C"? Round your answers as percentages to one decimal place. (Enter your answers from smallest to largest.)

To receive a "C" a score between % and % would be needed.

A 1.5 standard deviations above the mean or higher B 0.5 to 1.5 standard deviations above the mean C within 0.5 standard deviation of the mean D 0.5 to 1.5 standard deviations below the mean F 1.5 standard deviations below the mean or lower

Explanation / Answer

a)
mean = 0 , s = 1
p(X < -1.3)
z =( x -mean) / s
= ( -1.3 - 0) / 1
= -1.3
P(X < -1.3) = P(Z < -1.3 ) = 0.0968

b)
z value for 60% = +/-0.253 By using z standard table

c)

mean =100 , s = 15 , x = 115

p(X >115)
z = ( x - mean) / s
= (115 - 100) / 15
= 1
p(X >115) = P(Z > 1) = 0.1587 = 15.9%

e)

mean = 69.1 , s = 2.65 , x = 74

P(X > 74)

z= ( x - mean) / s
= (74 - 69.1) / 2.65
= 1.849
p(X > 74) = P(Z > 1.849) = 0.0322

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