Question

The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with standard deviation σ = 20 hours. A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. We wanted to be 95% confident that the error in estimating the mean life is less than 5 hours. What sample size should we use? Round z-value to two decimal places in your intermediate calculations. Round your answer up to the nearest whole number.

Answer 1

62 is the minimum sample size needed

Explanation:

We know that the population is approximately normally distributed so we will use a z-score for 95% confidence, which is 1.96. We are given the population standard deviation of σ = 20, and are given that the error should be 5 or less hours. The fact that it gives us sample data is irrelevant since we are told the population is approximately normally distributed and are given the population standard deviation.

See the attached photo for the calculation of the minimum sample size