For those intending to major in Business, quantitative GRE scores are normally d

Question

For those intending to major in Business, quantitative GRE scores are normally distributed with mean 152 and variance 64. Let Y denote a randomly selected quantitative GRE score. Use this to answer the following questions (Note: in order to answer following questions, you need to know the standard deviation using the formula: s=)

                                                                   

Use software to find P(Y 150). Be sure to paste your output.

Minitab: Calc > Probability Distributions > Normal.

Minitab Express: Statistics > Probability Distributions > CDF/PDF > Cumulative (CDF).

Write a sentence interpreting the value you found above. You should write the sentence so that it makes sense to someone not taking a statistics course.

A certain university will only consider admitting applicants who have a quantitative GRE of at least 150. Use your answer from part a to find the probability that a randomly selected Business applicant will be considered for admittance.

  Use software to find the probability that an intended Business major scores between 140 and 160 on the quantitative GRE. Paste the output. [ Hint: P(140 < Y 160) = P(Y 160) – P(Y 140)]

Using the Normal Probability table to answer the following questions.

i. [2 pts] Calculate the z-score of Y = 150. Round to two decimal places.

[Hint: See the “Finding Cumulative Probabilities” page of the online notes.]

ii. [2 pts] Use the normal probability table and find your answer to part i to find P(Y 150)

iii. [2 pts] if we know a student’s standardized score (z score) is 1, what is quantitative GRE scores for this student? [Hint: you need to transform z score to the raw score]

iv. [2 pts] Find the probability or proportion of scores between 145 and 172.

[Hint: you need to calculate z score for 145 and 172 and then look for the proportions of two z scores in the table, and then take the difference between two proportions. P (145 Y 172, see question d)

A prestigious university will only considering admitting Business students who scored in at least the 80th percentile of the quantitative GREs. What is the minimum score would you need to get in order to be considered for admittance into the university? You may use software or the normal probability table to find the answer.

y) = .80]

Explanation / Answer

Nearly 40.13% of the people will have mean below 150 in GRE scores

Prob for admission = 0.4013

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If z score = 1, then x = 152+1(8) = 160

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P(145<x<172) = P(-0.625<z<2.5)

=0.2357+0.4938

= 0.7295

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80th percentile z value = 0.84

y = 152+0.84(8)

=158.72

GRE scores Normal Mean 152 std dev 8 y=150 Z -0.25 p(Z<-0.25) 0.4013

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