Question

The wall thickness of 25 aquariums was measured by a quality-control engineer. The sample mean was xˉ=3.54 millimeters, and the sample standard deviation was s=0.17 millimeters. Compute a 95% tolerance interval on the glass-wall thickness that has the confidence level of 95%. Round your answers to two decimal places (e.g. 98.76).

Answer 1

To compute a 95% tolerance interval on the glass-wall thickness, you can use the formula: Tolerance Interval = sample mean ± (t-value)(sample standard deviation). The 95% tolerance interval for the glass-wall thickness is approximately 3.19 mm to 3.89 mm.

Step-by-step explanation:

To compute a 95% tolerance interval on the glass-wall thickness, we use the formula:

Tolerance Interval = sample mean ± (t-value)(sample standard deviation)

Since the sample size is 25 and the desired confidence level is 95%, we need to find the t-value with 24 degrees of freedom.

Using a t-table or a t-distribution calculator, we find that the t-value for a 95% confidence level and 24 degrees of freedom is approximately 2.064.

Substituting the values into the formula:

Tolerance Interval = 3.54 ± (2.064)(0.17)

Calculating the upper and lower limits:

Lower limit = 3.54 - (2.064)(0.17)

Upper limit = 3.54 + (2.064)(0.17)

Rounding the limits to two decimal places:

Lower limit ≈ 3.19 mm

Upper limit ≈ 3.89 mm

Therefore, the 95% tolerance interval for the glass-wall thickness is approximately 3.19 mm to 3.89 mm.