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
Hi there! The formula for circumference is π * diameter. Diameter is the length across the circle and twice the length of the radius.The radius is 5.4, so we will multiply that by 2 to get 10.8. The diameter is 10.8 inches. Now, multiply that numebr by 3.14 to find the circumference. 10.8 * 3.14 is 33.912 or 33.9 when rounded to the nearest tenth. There. The circumference is approx. 33.9 inches.
