The National Assessment of Educational Progress (NAEP) includes a mathematics test for high school seniors. Scores on the test ranges from 0 to 300. Suppose the standard deviation of the NAEP math score for 12th graders nationally is 35.
If you take a SRS of 50 12th-graders, and find out their average grade is 145, what is the 95% confidence interval of the average NAEP math score? If you take a SRS of 100 12th-graders, and find out their average grade is 145, what is the 95% confidence interval of the average NAEP math score?

picture below

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

    -7                           -7

2x is greater than 10

divide by 2 each side

x is greater than 5

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