Question

These are the scores of 40 students in MAT that took the Final Exam. Perform the computations asked below with this set of data:

88	91	50	65	46	99	72	82	66	75
70	58	86	83	68	82	59	98	64	82
99	58	20	63	64	39	81	89	96	101
83	56	93	84	70	22	105	81	102	77

1. What is the class mean of the test scores? Round to the nearest whole number.

2. What is the standard deviation (Sx) of the scores? Round to the nearest tenth.

3. What is the range of the scores?

4. What is the median?

5. What is the five number summary? Round each number to the nearest tenth.

6. The scores are roughly normally distributed. Calculate the interval that 68% of the data values fall between. Round to the nearest whole number.

Type answer as #1 to #2. Example: 65 to 76

7. Suppose a student got a 71 on the exam. Calculate a z-score, to two decimal places, for this student.

8. Describe the z-score according to its relationship to the mean (steps above/below).  

Select one:

a. The z-score is .15 steps above the mean.

b. The z-score is .15 steps below the mean.

c. The z-score is 20.5 steps below the mean.

d. The z-score is 20.5 steps above the mean.

9. What percentile is the student in? Round to the nearest whole number.

10. What does the student percentile represent?

Select one:

a. The student earned a higher score than 44% of the other students in the class.

b. 44% of the students passed the exam.

c. 44% of the students earned a higher score than the student.

d. The student has a 44% chance of passing the exam.

Answer 1

((1)	mean=	74.2 ( nearest whole number is 74)
(2))	SD=	21.8

here population standard deviation is calculated

(3)	Raange=max-min=	85
(4)	median=	79

(5) the five number summary are

min=	20
Q1=	63.75
median=	79
Q3	88.25
max=	105

(6) required range (52.2,95.8)

here we want to find the value x1 and x2 such that P(x1<X<x2)=0.68  

now we use standard normal variate z=(x-mean)/SD

for this first we find z1 and z2 such that P(z1<Z<z2)=0.68 and

this imply P(z1<Z<z2)=P(Z<z2)-P(Z<z1)=0.68

or, 1-P(Z<z1)-P(Z<z1)=0.68 ( since Z is symmetric)

or, P(Z<z1)=0.16 and z1=-1 and x1=mean+z1*SD=74.2-1*21.8=52.4

and z2=1 and x2=74.2+21.8=96

(7) for x=71, z=(x-mean)/SD=(71-74.2)/21.8=-0.15

(8)b. The z-score is .15 steps below the mean.

(9) percentile=100*P(Z<-0.15)=100*0.56=56

(10)c. 44% of the students earned a higher score than the student