Question

THINKING/COMMUNICATION 7. A post-secondary class has 600 students. The mean grade on their midterm exam is 70%, with a standard deviation of 15. a. Find the Z-score of a student who scored 80% on his exam. [2 marks] b. Find the percentage of students who failed the exam. [3 marks] c. How many students failed the exam (i.e. scored less than 49%)? [1 mark] d. Your friend claims he scored in the 99th percentile on his exam. What mark must he have achieved in order to do so? If this is impossible, be sure to explain why. [3 marks)

Answer 1

الب N = 600 Mean Cu) = 0.70 S.D CO-)= 15 Normal Distribution, As this follows a Z-score X-M olun la X=0.80 Z-score =0.80 -0.70 0.163 = 15/, боо b . People who failed - are the ones who scores less than 49.10. PCX < 0.49) = P(Z < 0.49-0.70 15/5500 prz<-0.343) Source - STATKEY P(Z <-0.343) = 0.366 (imape attacked) ] so, percentage of students who failed the exam the exam is 36.6% © No No. of students who 36.6% of 600 of failed the exam 36.6 100 Х 600 = 219.6 220 Capproximately) Sog ro, 220 students failed the exam .

d.) P-value 0.99 Z Z-sure from the p-value 2.327 [ Source - STATKEY limage attacked) Z= x - u s 2.327 = * -0.7 15 'shoco 1600 xب or X = 2.125 212.5.1 This is impossible to obtain as the greiding monks 100% his friend got 212.50%. and are only from 0% to le the Z-score (is Negative Z-sce indicates the stucent got less than 0.70% [Because for the mean, is exactly 0] to his classmates, he is one among (i) compared the people who sured in the lower half the class, ie, of to 50% of his classmates of

Statkey Theoretical Distribution Normal Distribution- Reset Plot Normal Distribution Left Tail Two-Tail Right Tail Mean Standard Deviation 0.40 0 1 0.35 Edit Parameters 0.30 0.25 0.20 0.366 0.15 0.10 0.05 0.00 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 -0.343 Activate Windows

Statkey Theoretical Distribution Normal Distribution Reset Plot Normal Distribution Left Tail Two-Tail Right Tail Mean Standard Deviation 0.40 0 0.35 Edit Parameters 0.30 0.25 0.20 0.990 0.15 0.10 0.05 0.00 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 2.327 Activate Windows

As this follows Normal Distribution, we use the formula mentioned. The p value and the z score from the p value is obtained from STATKEY (image attached for reference).