We need to find out how many adults must the brand manager survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage.
From the given data we know that our confidence level is 90%. From Standard Normal Table we know that the critical level at 90% confidence level is 1.645. In other words,
.
We also know that E=5% or E=0.05
Also, since,
is not given, we will assume that
=0.5. This is because, the formula that we use will have
in the expression and that will be maximum only when
=0.5. (For any other value of
, we will get a value less than 0.25. For example if,
is 0.4, then
and thus,
.).
We will now use the formula

We will now substitute all the data that we have and we will get



which can approximated to n=271.
So, the brand manager needs a sample size of 271
We are given
P = <span>$1,945.61
r = 11.2%
Amin = $156
A = $300
First, we convert the interest to effective monthly terms
i = 11.2%/12 = 0.933%
After one month, the interest saved by paying more than the minimum is
</span>(0.00933) (300 - 156) = $1.35
Answer:(A²-B²) = (A-B)² + 2AB
Step-by-step explanation: