ANSWER

EXPLANATION
The given inequality is,

By the definition of absolute value,

We divide through by negative 1, in the first part of the inequality and reverse the sign to get,

We simplify now to get,


Divide through by 2 to obtain,
Answer:
0.0035289
Step-by-step explanation:
From the question;
mean annual salary = $63,500
n = sample size = 31
Standard deviation = $6,200
Firstly, we calculate the z-score of $60,500
Mathematically;
z-score = x-mean/SD/√n = (60500-63500)/6200/√(31) = -2.6941
So we want to find the probability that P(z < -2.6941)
We can get this from the standard normal table
P( z < -2.6941) = 0.0035289
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
Answer:
8.5
Step-by-step explanation: