UNIT 5 HOMEWORK
Math 102 & Core 143
Note: All data below is ficticious.
1. You have list of 1000 data that have been entered into Excel. You then enter a formula to
convert these into standard units. You notice that the first 10 values for the conversion are:
8.2,2.3,4.5,−.3,−.8,−6.1,5.5, .2,1.1,4.7.
You immediately check your formula and discover a mistake. How did you catch it so quickly?
There are 5 numbers more than 4 SD’s away from the mean. This is much more than expected
since it is highly unlikely for a data point to be more than 4 SD’s away from the mean.
2. The average on a new IQ test is 100. Assuming that these IQ scores follow a Normal
distribution, if 1% of the population has scores over 135 on this test, what is the SD for scores
on this test?
In standard units, z≈2.33 has 1% of the data to its right (look up 98% in between −zand z).
Hence, set 135 −100
SD = 2.33.
From here, we get SD ≈15.
3. Suppose weekly CD sales at the Colgate Bookstore can be approximated by a normal distri-
bution with an average of $1690/wk and an SD of $160/wk.
a) What percentage of weeks have sales of more than $1850?
We convert 1850 to standard units: 1850−1690
160 = 1. Looking up z= 1 on the chart gives about
68% between −1and 1. Hence, about 16% of sales are more than $1850.
b) What sales level corresponds to the 29th percentile?
We want to look up 100−2(29) = 42% on the chart. This gives z≈ −.55. Hence, X−1690
160 =−.55
and we get that the desired percentile is X= $1602.
4. On my last exam, the average was 88 (out of 100) and the SD was 8.1. However, the data
did not follow the Normal curve; it was right-sided. True or false: there was something wrong
with the test. Explain.
No, not all distributions need be Normal. This was either an easy test or was a test taken by a
very good class.
