Given a population with
μ
= 30 and
σ
=
5,
1. What proportion of the data are higher than
32.5?
2. At what value is the 25th percentile?
3. What percent of the data are higher than 24?
4. What value is exactly 60 percent of the data lower then?
5. What percent of the data falls between values of 32 and 35?
6. What value is below exactly 10 percent of the data?

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Given a population with
μ
= 30 and
σ
=
5,
1. What proportion of the data are higher than 32.5?
Convert to z-value: z =
(x-μ)/
σ
= (32.5-30)/5 = .5
?
x:
30
32.5
z:
0
.5
Either: For z = .5 in column A, lookup the corresponding area from column C: .3085
Or:
For z = .5 in column A, lookup the corresponding area from column B: .1915
.5 - .1915 = .3085
2. At what value is the 25th percentile?
.25
x:
?
30
z:
?
0
For an area of .25in column C, lookup corresponding z score in column A: ~.67
Take negative, -.67
Convert z-score to data value, x = (z)(
σ
) + μ = (-.67)(5) + 30 =
26.65