Suppose probation officer caseloads have a mean of 115 offenders and a standard deviation of 10. Assuming caseload sizes are normally distributed, determine
a. the probability that a particular probation officer has a caseload between 90 and
105.
b. the probability that a particular probation officer has a caseload larger than 135.
c. the probability that four probation officers have a caseload larger than 135.
What would be an ideal response?
a.
1 2
90 115
10
2.5
105 115
10
1
.4938 .3413 .1525
x
z
x
z P
?
?
?
?
?
=
?
=
= ?
?
=
?
=
= ?
= ? =
b.
135 115
10
2
.0228
x
z P
?
?
?
=
?
=
= ?
=
c.
P = = (.0228)(.0228)(.0228)(.0228) .00000027
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