A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the standard deviation to be 1.3. He thinks the mean is 5.5 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.1 at the 95% level of confidence? Round your answer up to the next integer.

649

Step-by-step explanation:

Given that

Mean number of dresses is 5.5

Standard deviation of the sample, S.D is 1.3

Margin of error, M.E is 0.1

Level of confidence is 95% or 0.95

The formula for margin of error, M.E is

Z * (S.D/√n) , where

Z = Value for level of confidence which is 1.96

Proceeding further, we have

0.1 = 1.96 * (1.3/√n)

0.1 = 2.548 / √n, making √n subject of formula, we have

√n = 2.548 / 0.1

√n = 25.48, squaring both sides

n = 25.48²

n = 649.23

Therefore the number of sample size we're looking for is n = 649.23, when rounded to the nearest integer, we have it to be 649

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.