Knowing the population standard deviation, a 95% confidence interval infers that the population mean is between 0 and 100% is within ±1.96 standard deviations of the sample mean is within ±1.96 standard errors of the sample mean is too large

within ±1.96 standard deviations of the sample mean

Step-by-step explanation:

A 95% confidence interval is found using the formula C = 1 - α, and some other stuff, but let's focus on that for now. Using the formula:

.95 = 1 - α

α = .05

If α = .05, that means a 2-sided confidence interval would be found using the sample mean and the Z-score Z(subscript α/2), or Z.₀₂₅ because α AKA .05 divided by 2 = .025. From there, you take this either to your calculator or a Z-table (or perhaps you have a chart that lists the common CI values), and see that for the area to be .025 beneath a standard normal curve, your Z value is ±1.96 ("plus or minus" because we're considering a 2-sided confidence interval).

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative