1.E.121. Here are the total scores of 10 students in an introductory statistics

Question

1.E.121. Here are the total scores of 10 students in an introductory statistics course. 62 93 54 76 73 98 64 55 80 71 Previous experience with this course suggests that these scores should come from a distribution that is approximately Normal with mean 72 and standard deviation 10. The grading policy says that the cutoffs for the other grades correspond to the fol ing: bottom 5% receive F next 15% receive D next 40% receive C, and next 30% receive B These cutoffs are based on the N(72, 10) distribution. (a) Give the cutoffs for the grades in this course in terms of standardized scores. (Round your answers to two decimal places.) Letter Grade Standardized Cutoff (b) Give the cutoffs in terms of actual total scores. (Round your answers to the nearest whole number.) Letter Grade Scoring Ranges o to (c) Do you think that this method of assigning grades is a good one? Give reasons for your answer.

Explanation / Answer

(a)

For grade F, we have p = 0.05

So, the corresponding z-score is: z < -1.64

For grade D, we have p = 0.05 to 0.20

So, the corresponding z-score is: -1.64 < z < -0.84

For grade C, we have p = 0.20 to 0.60

So, the corresponding z-score is: -0.84 < z < 0.25

For grade B, we have p = 0.60 to 0.90

So, the corresponding z-score is: 0.25 < z < 1.28

(b)

Data given:

Mean, m = 72

Standard Deviation, S = 10

Using formula:

z = (X-m)/S

So,

X = S*z + m = 10*z + 72

We will be calculating cut off scores from z-scores using the above formula.

For grade F: z < -1.64

Scoring range for F grade : 0 to 10*(-1.64) + 72 , which equates to : 0 to 55.6

For grade D: -1.64 < z < -0.84

Scoring range for F grade : 10*(-1.64) + 72 to 10*(-0.84) + 72 , which equates to : 55.6 to 63.6

For grade C: -0.84 < z < 0.25

Scoring range for F grade : 10*(-0.84) + 72 to 10*(0.25) + 72 , which equates to : 63.6 to 74.5

For grade B: 0.25 < z < 1.28

Scoring range for F grade : 10*(0.25) + 72 to 10*(1.28) + 72 , which equates to : 74.5 to 84.8

Hope this helps !

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.