Answer: the sample size should be 39
Step-by-step explanation:
The sample mean is the point estimate for the population mean. Confidence interval is written as
Sample mean ± margin of error
Margin of error = z × σ/√n
Where
σ = population standard Deviation
n = number of samples
z represents the z score corresponding to the confidence level
From the information given,
σ = 4 minutes
Margin of error = 75 seconds. Converting to minutes, it becomes 75/60 = 1.25 minutes
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Therefore,
1.25 = 1.96 × 4/√n
1.25/1.96 = 4/√n
0.6378 = 4/√n
√n = 4/0.6378 = 6.27
n = 6.27² = 39
