If u are trying to solve for x is that x=2
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
Provided the 2% interest rate. The interest itself over a period of 4 years, compounds to $300. Thus, the total interest plus the cost of the fitness equipment would be a total of, $4,050.
2/3 of 480 is 480 divided by 3 and that number times 2, which is 320. The man or woman probably used $60 of this to buy the tea set, which leaves them with $260.
The answer is C. 60. If you add 14+19+16+11 it equals 60.
