So we are given that the mean is 42% and the sd (standard deviation) is 8%
Assuming our data is normal we can use the 68-95-99 rule
So one thing you should realize is that 42% + 8% is 50% which is passing. That is one standard deviation higher. So we use:
100 - 68 - 13.5 - 2.35 - 0.15 = 16. That means 16% of students passed the test. Which is terrible. They probably need to hit the books more.
Anyways if you have any question feel free to message me!
Hopes this helps!
4(2x raise to power 2-4-7x)
Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,
μ = 97
Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is
σ = 17/√n
We want to be 95% certain
97 - 5 ≤ x ≤ 97 + 5
By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that
μ - 2σ ≤ x ≤ μ + 2σ
Comparing to what we want, that's means we have to solve
2σ = 5
2 (17/√n) = 5
√n = 2 (17/5)
n = (34/5)² = 46.24
We better round up.
Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean
Answer:
13.708
Step-by-step explanation:
