PROBLEM 3: The average grade point average (GPA) of undergraduate students in Ne

Question

PROBLEM 3:

The average grade point average (GPA) of undergraduate students in New York is normally distributed with a population mean of 2.5 and a population standard deviation of .5.

(I) The percentage of students with GPA's between 1.3 and 1.8 is:     (a) less than 5.6%     (b) 5.7%    (c) 5.9%      (d) 6.2%      (e) 6.3%       (f) 6.6%      (g) 7.3%     (h) 7.5%    i) 7.9%      (j) more than 8%.

Choice

(II) The percentage of students with GPA's above 3.0 is:

Percentage

(III) Above what GPA will the top 5% of the students be (i.e., compute the 95th percentile):     

GPA

(IV) If a sample of 25 students is taken, what is the probability that the sample mean GPA will be between 2.50 and 2.75? (a) less than .10     (b) .122      (c) .243      (d) .307      (e) .346    (f) .38   (g) .42     (h) .44    (i) .494     (j) more than .494.

Choice

Choice

Explanation / Answer

Compute the z score by substituting Xi=1.3 and 1.8, Xbar=2.5 and s=0.5 to compute the two z scores respectively.

z1=(Xi-Xbar)/s=(1.3-2.5)/0.5=-2.4

z2=(1.8-2.5)/0.5=-1.4

Find the area corresponding to z scores and subtract the smallest from the largest.

0.0808-0.0082=0.0726 (choice g, 7.3)

ii)

Find z score using Xi=3

z=(3-2.5)/0.5=1

The required probability is area corresponding to z score that is 0.8413

iii)

z=0.05, Xbar=2.5, s=0.5 compute the Xi value.

0.05=(Xi-2.5)/0.5

Xi=2.525

iv). Apply th esame z score formula and obtain the z score corresponding to 2.50 and 2.75

z1=0 and z2=0.5

The areas corresponding to z scores are 0.5 and 0.6915.

Therefore, the required probability is 0.6915-0.5=0.1915

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