Confidence Interval for the Mean

The confidence interval for the mean of a population with a confidence level (1 − α) is:

Confidence Interval for the Mean

X is the mean of a sample of size n.

σ is the standard deviation of the population.

The maximum error is:

Maximum Error Formula

The larger the sample size, n, the lower the error.

The sample size is:

Sample Size Formula

Example

The time it takes for a supermarket cashier to serve customers follows a normal distribution with an unknown mean and a standard deviation of 0.5 minutes. From a random sample of 25 customers, the average time is 5.2 minutes.

1.Calculate the confidence interval at 95% for the average time it takes to serve customers.

Confidence Level Graph

For a confidence level of 95%, the critical value is zα/2 = 1.96.

Confidence Level Operations

2.Indicate the sample size needed to estimate the average time with an error of ± 0.5 minutes and a confidence level of 95%.

Sample Size Solution

n ≥ 4