Assuming that the normal heart rate in normal healthy individuals is normally distributed with mean 70
and standard deviation 10 beats per minute. Which heart rates are in the
a. top 5%?
b. middle 30%
c. lower 27%
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(a) Here they want you determine z-score on the number line such that the area under the given
normal curve be 5% to the RIGHT of this score or (which is the same) 95% to the LEFT of this score.
So, use the standard function invNorm of your regular calculator TI-83/84
area mean SD <<<---=== formatting pattern
z = invNorm(0.95, 70, 10).
Get the answer z = 86.45, which you should/can round to 87, the closest greater integer.
The z-scores under the problem's question are z >= 87.
Alternatively, you may use an online calculator
https://onlinestatbook.com/2/calculators/inverse_normal_dist.html
for this purposes.
(b) Here they want you determine z-scores z1 and z2 on the number line such that the area under the given
normal curve be 65% to the left of the z1-score and 35% to the left of the z2-score.
So, use the standard function invNorm of your regular calculator TI-83/84
area mean SD
z1 = invNorm(0.65, 70, 10) = 73.85, z2 = invNorm(0.35, 70, 10) = 66.15
Get the answer 66 <= z <= 73.
The numbers 35 and 65 came from 50 % +- %.
Alternatively, you may use an online calculator
https://onlinestatbook.com/2/calculators/inverse_normal_dist.html
for this purposes.
(c) Here they want you determine z-score on the number line such that the area under the given
normal curve be 27% to the LEFT of this score.
So, use the standard function invNorm of your regular calculator TI-83/84
area mean SD <<<---=== formatting pattern
z = invNorm(0.27, 70, 10).
Get the answer z = 63.87, which you should/can round to 63, the closest lesser integer.
The z-scores under the problem's question are z <= 63.
Alternatively, you may use an online calculator
https://onlinestatbook.com/2/calculators/inverse_normal_dist.html
for this purposes.
Solved.
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If you are a beginner student in such calculations, I advise you to start using the online calculator,
since it has simple intuitively clear interface and shows the area of the interest.
So, you will never make errors and will learn quickly and effectively the meaning of such calculations.