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The mean height of a population of girls aged 15 to 19 years in a certain population
was found to be 165 cm with a standard deviation of 15cm.
Assuming that the heights are normally distributed, find the heights in centimeters
that correspond to the following percentiles:
a. Between the 20th and 50th percentiles.
b. Between the 40th and 60th percentiles.
c. Between the 10th and 90th percentiles.
d. Above the 80th percentile.
e. Below the 10th percentile.
f. Above the 5th percentile.
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Using function invNorm of TI-83 or TI-84 calculators
(see the instructions in this web-site https://www.statology.org/invnorm-ti-84/)
(a) Between the 20th and 50th percentiles.
Find the marks for the given normal curve
corresponding to values of the cumulative probabilities 0.2 and 0.5.
probability mean SD <<<---=== format
The lover mark for the height is invNorm( 0.2, 165, 15) = 152.4 cm (rounded).
The upper mark for the height is invNorm( 0.5, 165, 15) = 165.0 cm (rounded).
ANSWER. The height is 152.4 cm <= h <= 165 cm.
(b), (c) are similar: do them in the same way.
(d) Above the 80th percentile.
Find the mark for the given normal curve
corresponding to value of the cumulative probabilities 0.8.
The mark for the height is invNorm( 0.8, 165, 15) = 177.6 cm (rounded).
ANSWER. The height is h >= 177.6 cm.
(e) Below the 10th percentile.
Find the mark for the given normal curve
corresponding to value of the cumulative probabilities 0.1.
The mark for the height is invNorm( 0.1, 165, 15) = 145.8 cm (rounded).
ANSWER. The height is h <= 145.8 cm.
(f) Above the 5th percentile.
Find the mark for the given normal curve
corresponding to value of the cumulative probabilities 0.05.
The mark for the height is invNorm( 0.05, 165, 15) = 140.3 cm (rounded).
ANSWER. The height is h <= 140.3 cm.
Solved.
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Alternatively, you may use an online calculator at this web-site
https://onlinestatbook.com/2/calculators/inverse_normal_dist.html
It shows the associated diagrams and makes the entire work more understandable.
So, if you are a beginner in study this subject, I recommend you
to start using this online calculator.
Later, when you will learn the subject enough, you may switch to calculators
TI-83, TI-84 back to be prepared to the exam's environment.