Download Self Assessment for Lesson 12 1 1. Click on “Begin Assessment

Self Assessment for Lesson 12
1. Click on “Begin Assessment” button.
2. Scroll down to begin quiz.
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Self Assessment for Lesson 12
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1. Which one of the following is a false statement about
a standardized value (z-score)?
It represents how many standard devations an observation lies from the mean.
It represents in which direction an observation lies
from the mean.
It is measured in the same units as the variable.
2. Rachael got a 670 on the analytical portion of the
Graduate Record Exam (GRE). If GRE scores are
normally distributed and have mean µ = 600 and
standard deviation σ = 30, what is her standardized
score?
Self Assessment for Lesson 12
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3. The length of human pregnancies from conception to
birth is known to be normally distributed with a mean
of 266 days and standard deviation of 16 days. What
proportion of pregnancies last between 250 and 274
days?
4. In a certain marathon, the average time to complete
the race was normally distributed with mean µ = 4.15
hours and standard deviation σ = 0.84 hours. If we
wanted to give medals to the 4% of the runners with
the best times, what would be the slowest time that
would receive a medal?
Self Assessment for Lesson 12
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5. Suppose the lengths of sport-utility vehicles (SUV)
are normally distributed with mean µ = 190 inches
and standard deviation σ = 5 inches. Marshall just
bought a brand-new SUV that is 194.5 inches long
and he is interested in knowing what percentage of
SUVs are longer than his. Using his statistical knowledge, he drew a normal curve and labeled the appropriate area of interest. Which picture best represents
what Marshall drew?
Plot B
0.4
0.4
Plot A
0.3
Area of
Interest
0.0
0.0
0.1
0.1
0.2
0.2
0.3
Area of
Interest
-4
-2
0
2
Standard Normal Curve
Plot A
4
-4
-2
0
2
Standard Normal Curve
Plot B
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Self Assessment for Lesson 12
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answers in green and wrong answers in red. For question
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Solutions to Quizzes
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Solutions to Quizzes
Solution to Quiz:
units of measure.
1. The z-score does not have any
End Quiz
Solutions to Quizzes
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Solution to Quiz: 2. To find standardized scores, you
use the following formula:
z=
x−µ
σ
In this case, it is found by
z=
670 − 600
= 2.33
30
End Quiz
Solutions to Quizzes
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Solution to Quiz: 3. First, draw the picture. Then find
the z-scores for both 250 and 274. The z-score for 250 is
found by 250−266
= −1. Similarly, the z-score for 274 is
16
274−266
=
0.50.
Now
go to the standard normal table and
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see that the area to the left of 0.50 is 0.6915. The area to
the left of −1 is 0.1587. Subtracting off the smaller area
gives the final answer of 0.6915 − 0.1587 = 0.5328.
End Quiz
Solutions to Quizzes
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Solution to Quiz: 4. First, draw the picture. Because
in racing, the smallest times are the best times, we want
that 4% to be on the left side of the mean. So we go to the
table and find the z-score that has area that is closest to
4%, or 0.0400. That z-score is −1.75. We can now use our
formula to solve for that time. So
z=
x − 4.15
= −1.75
0.84
and by solving this for x we find that the time you would
have to have would be 2.68 hours.
End Quiz
Solutions to Quizzes
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Solution to Quiz: 5. Because we are looking for the
probability of being greater than z = 0.90, we need to
choose the area on the right. That area is correctly identified in Plot B.
End Quiz