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2 years ago

IQ scores are normally distributed with a mean of 100 and a standard deviation of 16.

Mathematics

1 answer:

Alenkasestr [34]2 years ago

8 0

Answer:

Given

μ = 100
σ = 16

x = 68

z = (x - μ)/σ =
(68 - 100)/16 = -2
z-score = 0.0228 = 2.28%

x = 100 and x = 132

z = (100 - 100)/16 = 0, z-score = 50%
z = (132 - 100)/16 = 2, z-score = 0.9772 = 97.72%
97.72% - 50% = 47.72%

68% confidence interval, assumed sample number n = 100

z-score representing 68% = 0.47

CI = μ ± z× σ/√n
CI = 100 ± 0.47*16/√100 =
= 100 ± 0.752

n = 10000
x = 148
z = (148 - 100)/16 = 3, z-score is 0.9987

Number of people scored above 148:

(1 - 0.9987)*10000 = 13 people

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That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are $a^{3}$ and $b^{3}$ . The difference of those two cubes is:
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In our problem, a = 4 (since $a^{3}$ = 64) and b = y (since $b^{3} = y^{3}$ . Plug these values into the rule to find the factor of $64 - y^3$ :
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