Standard deviation Question- BC

[belmont3]

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The average IQ of the city of Gotham is 110, and the standard deviation is 15. If the city has a population of 15,000, what would be a reasonable number of people whose IQ is above 140?

150 people
B. 225 people
C. 375 people
D. 450 people
E. 750 people

The answer is choice C. BC explanation is way too hard to grasp. Does anyone know to solve this question in a simple/ simpler way? Thank you!!

 

[StumpMT]

Mean is 110 and SD is 15 so 1SD from mean is 95 and 125 and 2SD from mean is 80 and 140. On a standard curve 95% of the population is within 2SD from the mean (2.5% below and 2.5% above. If the population is 15000 then 2.5% of 15000 is above IQ of 140. 2.5% is 1% + 1% + 0.5%. 1% of 15000 is 150. 2.5% = 150+150+75=375.

 

[belmont3]

Mean is 110 and SD is 15 so 1SD from mean is 95 and 125 and 2SD from mean is 80 and 140. On a standard curve 95% of the population is within 2SD from the mean (2.5% below and 2.5% above. If the population is 15000 then 2.5% of 15000 is above IQ of 140. 2.5% is 1% + 1% + 0.5%. 1% of 15000 is 150. 2.5% = 150+150+75=375.

How did you get the 2.5%?

 

[StumpMT]

How did you get the 2.5%?

95% is within 2SD of mean which means that 5% is outside of 2SD. Since not all 5% can be greater than 2SD from the mean, 2.5% is below 2SD from the mean and 2.5% is above 2SD from the mean (2.5+2.5=5).

 

[belmont3]

95% is within 2SD of mean which means that 5% is outside of 2SD. Since not all 5% can be greater than 2SD from the mean, 2.5% is below 2SD from the mean and 2.5% is above 2SD from the mean (2.5+2.5=5).

Oh okay. Got it 🙂 Thank you Thank you!!