Instructions: Read the scenario and answer the questions below. Round all probab
ID: 3052999 • Letter: I
Question
Instructions: Read the scenario and answer the questions below. Round all probabilities and proportions to 4 decimal places.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 8.8. (Source:www.ets.org). A graduate school requires that students score above 160 to be admitted.
What is the probability that a randomly selected student will score less than 150 points? What is the percentile rank of a student who earns a quantitative GRE score of 142? Historically, Depart of History at NYU has admitted students whose quantitative GRE score is at least at the 61st percentile. (Source: history.fas.nyu.edu/object/admissions.faq.html.) What is the lowest GRE score of the students they admit? Determine the 80th percentile of combined GRE scores. Determine the combined GRE scores that make up the middle 95% of all scores? Use the standard normal distribution to determine the following:
68% of the scores lie between what two values? 95% of the scores lie between what two values? 99% of the scores lie between what two values? Instructions: Read the scenario and answer the questions below. Round all probabilities and proportions to 4 decimal places.
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 8.8. (Source:www.ets.org). A graduate school requires that students score above 160 to be admitted.
What is the probability that a randomly selected student will score less than 150 points? What is the percentile rank of a student who earns a quantitative GRE score of 142? Historically, Depart of History at NYU has admitted students whose quantitative GRE score is at least at the 61st percentile. (Source: history.fas.nyu.edu/object/admissions.faq.html.) What is the lowest GRE score of the students they admit? Determine the 80th percentile of combined GRE scores. Determine the combined GRE scores that make up the middle 95% of all scores? Use the standard normal distribution to determine the following:
68% of the scores lie between what two values? 95% of the scores lie between what two values? 99% of the scores lie between what two values? Instructions: Read the scenario and answer the questions below. Round all probabilities and proportions to 4 decimal places.
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 8.8. (Source:www.ets.org). A graduate school requires that students score above 160 to be admitted.
What is the probability that a randomly selected student will score less than 150 points? What is the percentile rank of a student who earns a quantitative GRE score of 142? Historically, Depart of History at NYU has admitted students whose quantitative GRE score is at least at the 61st percentile. (Source: history.fas.nyu.edu/object/admissions.faq.html.) What is the lowest GRE score of the students they admit? Determine the 80th percentile of combined GRE scores. Determine the combined GRE scores that make up the middle 95% of all scores? Use the standard normal distribution to determine the following:
68% of the scores lie between what two values? 95% of the scores lie between what two values? 99% of the scores lie between what two values?
Explanation / Answer
Ans:
Given that
mean=150
standard deviation=8.8
1)
z=(150-150)/8.8=0
P(x<150)=P(z<0)=0.5
2)z=(142-150)/8.8=-0.909
P(z<=-0.909)=0.1817
So,18th percentile approximately
3)P(Z<=z)=0.61
z=0.2793
lowest score=150+0.2793*8.8=152.458
4)P(Z<z)=0.8
z=0.8416
x=150+0.8416*8.8=157.406
5)lower limt=150-1.96*8.8=132.75
uppwr limit=150+1.96*8.8=167.25