Math 4 – Z- Score Word Problems HW & Equations of R.F. Review
Name: _________________________
1. A patient recently diagnosed with Alzheimer's disease takes a cognitive abilities test. The patient scores a 45 on
the test (µ = 52, σ = 5). What is this patient's percentile rank?
2. Another patient with Parkinson's disease takes the same cognitive abilities test as in question 1 and scores a 54.
What percent of individuals would receive a higher score?
3. A fifth grader takes a standardized achievement test (µ= 125, σ = 15) and scores a 148. What is this child's
percentile rank?
4. Pat and Chris both took a spatial abilities test (µ = 80, σ = 8). Pat scored a 76 and Chris scored a 94. What percent
of individuals would score between Pat and Chris?
5. What percentage of a normal population are more than 1.5 standard deviations above the mean?
In problems 6 - 15, let us assume that the mean of the general population, µ, is equal to 100 on a standard I.Q. test and
the standard deviation, σ, is 12. It is assumed that the variable is normally distributed.
Salley obtains a score of 101 on an I.Q. test.
6. What percent of cases fall between her score and the mean?
7. What is the area that falls above her score?
8. What is her percentile rank in the general population?
Matt obtains a score of 96 on this I.Q. test.
9. What percent of cases fall between his score and the mean?
10. What is the area that falls above his score?
11. What is his percentile rank in the same general population?
12. What percent of cases in the distribution fall between both Salley and Matt’s scores (i.e., 101 and 96,
respectively)?
13. What percent of the area under the normal curve falls between a score of 81 and 84?
14. What are the percentile ranks of each of these two scores?
15. What is the probability of obtaining a case that falls in the range between z = -1.58 and z = -1.33
---------------------------------------------------------------------------------------------------------------------------------------------For each problem find the following: x - & y – intercept(s), vertical asymptote(s), horizontal asymptote, slant
asymptote, holes, and domain.
16.
x2  x
f ( x)  3
2x  4 x 2  6 x
x-int: _____________________
y-int: _____________________
hole: _____________________
V.A.: _____________________
H.A.: _____________________
S.A.: _____________________
Domain: __________________
---------------------------------------------------------------------------------------------------------------------------------------------17.
m(x) 
4 x2  9
2x  2
x-int: _____________________
y-int: _____________________
hole: _____________________
V.A.: _____________________
H.A.: _____________________
S.A.: _____________________
Domain: __________________
---------------------------------------------------------------------------------------------------------------------------------------------18.
k( x ) 
2x  5
2 x  5x  7
x-int: _____________________
2
y-int: _____________________
hole: _____________________
V.A.: _____________________
H.A.: _____________________
S.A.: _____________________
Domain: __________________
----------------------------------------------------------------------------------------------------------------------------------------------------------1. 8.08%
2. 34.46%
3. 93.70%
4. 65.14%
5. 6.68%
9. 12.93%
10. 62.93%
11. 37.07%
12. 16.12 %
13. 3.47%
16.
17.
18.
6. 3.19%
7. 46.81%
14. 5.71% & 9.18%
8. 53.19%
15. 0.0410
x-intercept
(-1,0)
y-intercept
None
V.A.
x = -3 & x = 1
Hole
x=0
H.A.
y=0
S.A.
None
Domain
(-3/2, 0) &
(3/2,0)
(-5/2,0)
(0,-9/2)
x = -1
None
None
y = 2x - 2
(, 3)  (3,0)  (0,1)  (1, )
(, 1)  (1, )
(0,-5/7)
x = -1 & x = 7/2
None
y=0
None
(, 1)  (1,7/2)  (7/2, )