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u = 3.0 with the standard deviation is 0.5. Assume that the random variable X (the GPA of a students selected randomly) is normally distributed. (a) Find the probability that the GPA of this student is between 2.8 and 3.4. (b) Find the probability that the GPA of this student is 0.5 above the mean, i.e. P(X > μ+0.5). (c) If the university offer scholarships to top 5 percent of students (i.e. 95 percentile), what is the required GPA of a student receiving this scholarship? what is the

u = 3.0 with the standard deviation is 0.5. Assume that the random variable X (the GPA of a students selected randomly) is normally distributed. (a) Find the probability that the GPA of this student is between 2.8 and 3.4. (b) Find the probability that the GPA of this student is 0.5 above the mean, i.e. P(X > μ+0.5). (c) If the university offer scholarships to top 5 percent of students (i.e. 95 percentile), what is the required GPA of a student receiving this scholarship? what is the

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 58CR
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The grade point average (GPA) of a college student at a large university is u = 3.0 with the standard deviation is 0.5. Assume that the random variable X (the GPA of a students selected randomly) is normally distributed. (a) Find the probability that the GPA of this student is between 2.8 and 3.4. (b) Find the probability that the GPA of this student is 0.5 above the mean, μ +0.5). i.e. P(X > (c) If the university offer scholarships to top 5 percent of students (i.e. 95 percentile), what is the required GPA of a student receiving this scholarship? (d) If a random sample of n probability the sample mean X = 25 students are selected from this university, what is the is between 2.8 and 3.4?
Transcribed Image Text:The grade point average (GPA) of a college student at a large university is u = 3.0 with the standard deviation is 0.5. Assume that the random variable X (the GPA of a students selected randomly) is normally distributed. (a) Find the probability that the GPA of this student is between 2.8 and 3.4. (b) Find the probability that the GPA of this student is 0.5 above the mean, μ +0.5). i.e. P(X > (c) If the university offer scholarships to top 5 percent of students (i.e. 95 percentile), what is the required GPA of a student receiving this scholarship? (d) If a random sample of n probability the sample mean X = 25 students are selected from this university, what is the is between 2.8 and 3.4?
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