Question

5. Some MATH323 test scores are standardized to a Normal distribution model with a mean of S+T and a standard deviation of F+L. Do 4 of the following parts only; mark the ones that you want graded by X.

a. ____ Determine the minimum score to be in the top 20% of all scores. Ans.___________

b. ____ If the term “A student” is used to describe a student whose score is in the top 10% of all scores. What is the range of scores for anyone who qualifies as an A student? Ans.___________

c. ____ Determine the proportion of “A student” score of at least 98. Ans.___________

d. ____ If the term “D student” is used to describe a person whose score is in the [µ-2σ , µ -1.2σ] range. What is the likelihood that a student failed? Ans.___________

e. ____ What percentage of students is expected to score above µ+1.25σ? Ans.___________

H = 6

T = 27

F = 3

L = 7

S = 47

Please do it correctly and need to show steps

Answer 1

The MATH323 scores follow normal distribution with mean S+T = 74 and standard deviation = 10

a) The minimum score to be in top 20% of all the scores is:

P(M>X) = 0.2

which gives the value of Z as 0.841621

The value of X is 82.42

b) The range of scores to qualify as A student can be given as follows:

P(M>X) = 0.1

which gives the value of Z as 1.281552

The range of A-students is (86.82, 100)

Using the fact that the maximum score can be 100

c) The proportion of students who score atleast 98% is

P(M>98)

The probability is 0.008198

The proportion of A students who earn at least 98% is 0.008198/0.1 = 0.082 or 8.2%

d) Assuming that a student fails if he/she scores less than D-student i.e. mu-2sigma or 74-20 = 54

So the probability that the student fails is:

P(M<54) = 0.02275 or 2.275%

e) The percent of students expected to score more than mu + 1.25*sigma is

P(M>86.5) = 0.10565 or 10.565%