Answer: 547
Step-by-step explanation: The margin of error formulae is given below as
Margin of error = critical value ×(σ/√n)
Where σ = standard deviation and n is the sample size.
From our question, margin of error = 0.08
Variance is 1.691,
hence σ = √variance = √1.691
= 1.3.
We will be using a z test for our critical value this is because a soft drink manufacturer will always produce drinks more than 30 in numbers.
The critical value for a 85% confidence interval is 1.44.
Hence critical value is 1.44.
By substituting the parameters, we have that
0.08 = 1.44 × 1.3/ √n
0.08 = 1.873/ √n
By cross multiplying
0.08 × √n = 1.873
√n = 1.873/ 0.08
√n = 23.41
n = (23.41)²
n = 547.
