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KEY
CORRECT SOLUTION IS UNDERLINED
______________________________
Exam 1
–
Part 1: Chapters 13
–
Math &146
–
Winter ’10 –
Gray
Instructions: Show work for each question.
Partial credit will be awarded based on work shown. This includes showing what was entered into the
calculator and sketching the Normal distributions.
To clarify the final solution, box it.
There is a 100 minute time limit. A graphing calculator
must be used.
Each problem is worth 4 points.
There are 4 extra credit points possible.
Assume all rounding to be at 4 decimal places
Problems 16
[4 points each]
The lengths of pregnancies in a small rural
village are Normally distributed with a mean of 265 days and a standard
deviation of 13 days.
1.
What proportion of pregnancies are longer than 275 days?
Normalcdf(275,1E9,265,13)=0.2208
2.
How many days is the cutoff for the top 10% of pregnancies?
Calculator input is percentage to left.
10% above is same as 90%
below.
invNorm(0.9,265,13)=281.6602 Days
3.
What proportion of pregnancies are longer than 250 days and
shorter than 280?
Nomalcdf(250,280,265,13)=0.7514
4.
Using the 689599.7 Rule, what pregnancies lengths make up the
middle 95%?
95% is
±2
°
265 ± 2
13
±
= 265 ± 26 =
239 to 291 days.
5.
Is this distribution considered a standard Normal distribution
?
Is
not, what mean and standard deviation would make it a standard
Normal distribution?
No,
standard Normal distributions have mean 0 and standard
deviation 1.
6.
Suppose Ana
’
s pregnancy lasted 270 days.
a.
What is her
z
score?
b.
If another woman in the hospital gave birth on the same day as
she did with a
z
score of 0, who conceived first?
?
=
?²−³
°
=
270
−
265
16
=
0.3846
0 < 0.3846
Ana conceived first.
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View Full DocumentExam 1
–
Math 146
–
Winter ’10 –
Gray
–
Page 2
Problems 78
A sample was taken of the verbal SAT scores of applicants
to a California State College. The following is a boxplot of the scores.
7.
What is the approximate scores for the middle 50% of the verbal SAT
scores above?
SOLUTION:
Verbal GRE scores from approximately 380 to 610.
Scores from 400 to 610 (or close are okay).
1 point off it student put approximately 480.
8.
State three other useful facts about the boxplot above.
In other
words, list three pieces of information you can gather from the plot.
SOLUTION:
A five point summary is good.
(Giving approximately
Verbal GRE scores is okay.)
Min:
280, Q1: 380, Med: 480, Q3: 520, Max: 770.
#10 SOLUTION:
Removing 1 data point will move the median very
little (it will still be in the interval 10 to 20.
However it will cause the
mean to drop as this data point is very high and influential.
(a) is the
best choice.
#11 SOLUTION:
Skewed right means that the median is left of the
mean.
So, (e) is the best choice.
Problems 711
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This note was uploaded on 10/15/2011 for the course SPAN 101103 taught by Professor All during the Fall '11 term at Tacoma Community College.
 Fall '11
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