Question

1. To FOUR DECIMAL PLACES: Determine the area under the standard normal curve that lies

1. to the left of Z = –1.31

2. to the right of Z = –2.47

3. between Z = –2.47 and Z = –1.31

4. between Z = 1.31 and Z = 2.47

2. Find the z-scores that separate the middle 84% of the standard normal distribution from the area in the tails.

3. Find z_0.18

4. a. Find the Z-score corresponding to the 72nd percentile. In other words, find the Z-score such that the area under the standard normal curve to the left is 0.72.

b.   How many standard deviations above the mean is the 72nd percentile?

5. The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation 9.8. (Source: http://www.ets.org/.) A graduate school requires that students score above 160 to be admitted.

1. What proportion of combined GRE scores can be expected to be between 150 and 160? Take your answer out to FOUR DECIMAL PLACES.
2. What is the probability that a randomly selected student will score over 140 points? Take your answer out to FOUR DECIMAL PLACES.

Answer 1

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(1)

ANSWER::-

AS FOR GIVEN DATA...

1. To FOUR DECIMAL PLACES: Determine the area under the standard normal curve that lies

1. to the left of Z = –1.31

1. to the right of Z = –2.47

1. between Z = –2.47 and Z = –1.31

1. between Z = 1.31 and Z = 2.47

ANS ::-

Area to the left of Z at -1.31 = 0.0951

Area to the right of Z at -2.47 = 1 - area to the left of z at -2.47

= 1 - 0.0068 = 0.9932

C) area between z= -2.47 and z =-1.31 = 0.0951-0.0068

= 0.0883

D) area betwen z=1.31 and z=2.47 = 0.0883

(3)

1. The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation 9.8. (Source: http://www.ets.org/.) A graduate school requires that students score above 160 to be admitted.

1. What proportion of combined GRE scores can be expected to be between 150 and 160? Take your answer out to FOUR DECIMAL PLACES.
2. What is the probability that a randomly selected student will score over 140 points? Take your answer out to FOUR DECIMAL PLACES.

ANS ::-

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