Answer:
n = 195
Explanation:
What sample size is necessary such that a 98% confidence interval for the mean, using σ = 3, has a width of pm±0.5?
We solve using Margin of error formula
= z × Standard deviation/√n
Margin of error = ± 0.5
Standard deviation = 3
n = ??
z = 2.326
Hence,
±0.5 = 2.326 × 3/√n
Cross Multiply
±0.5 × √n = 6.978
√n = 6.978/±0.5
√n = ±13.956
Square both sides
n = (±13.956)²
n = 194.769936
Approximately = 195 samples