This preview shows pages 1–5. Sign up to view the full content.
zScore
3.50
0.00023
0.02%
3.25
0.00058
0.06%
3.00
0.00135
0.13%
2.75
0.00298
0.30%
2.50
0.00621
0.62%
2.25
0.01222
1.22%
2.00
0.02275
2.28%
1.75
0.04006
4.01%
1.50
0.06681
6.68%
1.25
0.10565
10.56%
1.00
0.15866
15.87%
0.75
0.22663
22.66%
0.50
0.30854
30.85%
0.25
0.40129
40.13%
0.00
0.50000
50.00%
0.25
0.59871
59.87%
0.50
0.69146
69.15%
0.75
0.77337
77.34%
1.00
0.84134
84.13%
1.25
0.89435
89.44%
1.50
0.93319
93.32%
1.75
0.95994
95.99%
2.00
0.97725
97.72%
2.25
0.98778
98.78%
2.50
0.99379
99.38%
2.75
0.99702
99.70%
3.00
0.99865
99.87%
3.25
0.99942
99.94%
3.50
0.99977
99.98%
Area to
the Left
Area to
the Left
This table is similar to the table used in our textbook.
Select any
cell under Column B to see the Excel formula used.
See the worksheet
Normal Ex
for an application example.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document y
Minutes
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Solution Method 1.
...............................
See Solution Method 2 at RIGHT
The time per workout an athlete uses a stairclimber is normally distributed, with a
mean of 20 minutes and a standard deviation of 5 minutes.
An athlete is randomly
selected.
a.
Find the probability that the athlete uses a stairclimber for less than 17 minutes.
b.
Find the probability that the athlete uses a stairclimber between 17 and 22
minutes.
c.
Find the probabiliity that the athlete uses a stairclimber for more than 22
minutes.
Solution:
First, we recall that a normal distribution extends approximately three
standard deviations above and below the mean.
Thus, the time on the stairclimber
will probably be within 3 standard deviations, or 3*5 = 15 minutes.
Thus, the
possible values of time will extend from 20  15 = 5 to 20 + 15 = 35.
We create a column of Minutes ranging from 5 to 35, in one minute increments.
(Use Edit > Fill > Series to create the list.)
This column is shown at right.
Next, use the NORMDIST function to generate a column of Area to the Left.
This
function has the format NORMDIST(x,mean,stddev,true).
In this case, the formula
for cell B12 will look like:
=NORMDIST(A12,20,5,true)
We then add another
column to covert to percentage.
Part A:
The answer is the area to the left of 17.
This is given in the Area to the Left
column.
Thus, simply look up x = 17.
That is, P(x<17) = 0.2743 = 27.43%.
Part B:
The answer is the area between 17 and 22.
Since the table gives Area to
the Left, we look up 22 and 17, then subtract the area.
(Answer will always be
positive, so be sure to subtract smallest from largest.)
That is, P(17<x<22) = 0.6554
 0.2743 = 0.3811 = 38.11%
Part C:
The answer is the area above 22.
Since the table gives Area to the Left (or
Area Below), we look up 22 and subtract the area from 1.
That is, P(x>22) = 1 
P(x<22) = 1  0.6554 = 0.3446 = 34.46%
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 0.0013
0.13%
0.0026
0.26%
0.0047
0.47%
0.0082
0.82%
0.0139
1.39%
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 07/15/2011 for the course MATH 221 taught by Professor Bethdodson during the Spring '10 term at DeVry Chicago.
 Spring '10
 BethDodson

Click to edit the document details