Answer: 113
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Step-by-step explanation:
- mu = 75 = mean, since it's at the center
- sigma = 8 = standard deviation (each gap between the tickmarks is 8 units wide)
From the given info, we see that 91 is two standard deviations above the mean. The diagram shows 91 is two tickmarks to the right of center. Or we could note that z = (x-mu)/sigma = (91-75)/8 = 2.
Roughly 95% of the normal distribution is within 2 standard deviations of the mean. I'm using the Empirical Rule.
So about 95% of the population is between 59 and 91 inches tall. That leaves 5% of the population in both tails combined. Cut this in half to get 2.5%
We have 2.5% of the population taller than 91 inches
2.5% of 4500 = 0.025*4500 = 112.5 = 113
Roughly 113 people are taller than 91 inches
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Side notes:
- The answer is approximate because the Empirical Rule is just a rough approximation of percentages; also, I rounded 112.5 to 113 (it makes no sense to have half a person).
- 59 inches = 4 ft, 11 in
- 75 inches = 6 ft, 3 in
- 91 inches = 7 ft, 7 in
- Roughly 95% of the population of NBA players is between 4 ft, 11 in and 7 ft, 7 in, according to this data set.