Suppose that at a large state university graduate research assistants are paid by the hour
Data from the personnel office show the distribution of hourly wages paid to graduate
students across the campus is approximately normal with a mean of $12.00 and a
standard deviation of $2.50. Determine
a. the percentage of graduate assistants who can earn an hourly wage of $15 or
more.
b. the probability of selecting at random from personnel files a graduate assistant
who earns an hourly wage of $15 or more.
c. the percentage of graduate assistants who earn between $10 and $12 per hour.
d. the probability of selecting at random from personnel files a graduate assistant
who earns between $10 and $12 per hour.
e. the percentage of graduate assistants who earn an hourly wage of $11 or less.
f. the probability of selecting at random from the personnel files a graduate
assistant who earns an hourly wage of $11 or less.
g. the probability of selecting at random from personnel files a graduate assistant
whose hourly wage is extreme in either direction – either $10 or below or $14 or
above.
What would be an ideal response?
a.
15 12
2.5
1.2
x
z
?
?
?
=
?
= =
The percentage of graduate assistants who can earn an hourly wage of $15 or
more is 11.51%.
b.
P = .1151
c.
10 12
2.5
.8
x
z
?
?
?
=
?
=
= ?
28.81% of graduate assistants earn between $10 and $12 per hour.
d.
P = .2881
e.
11 12
2.5
.4
x
z
?
?
?
=
?
= =
?
34.46 % of graduate assistants earn less than $11 per hour.
f.
P = .3446
g.
14 12
2.5
.8
10 12
2.5
.8
(2)(.2119) .4238
x
z
x
z P
?
?
?
?
?
=
?
= =
?
=
?
=
= ?
= =
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