A sample of 87 glass sheets are measured for thickness. They have a sample mean of 4.20 mm and a sample standard deviation of 0.10 mm. What is the level of the confidence interval (4.185, 4.215)?

83.85%

Step-by-step explanation:

The formula for confidence interval

= Mean ±( z × Standard deviation/√n)

Confidence Interval = Mean ± Margin of Error

Mean = 4.20mm

n = 87

Standard deviation = 0.10mm

z =

Hence:

Confidence Interval = Mean ± Margin of Error

Step 1

We find the Margin of Error

(4.185, 4.215) = 4.20 ± Margin of Error

4.20 - 4.185 = 0.015

4.215 - 4.20 = 0.015

Hence, Margin of Error = ± 0.015

Step 2

We find the z score

Margin of Error = z × Standard deviation/√n

±0.015 = z × 0.10/√87

± 0.015 = 0.0107211253z

z = ±0.015/0.0107211253

z = 1.39910686428

z score ≈ 1.4

Step 3

We find the confidence interval that corresponds to 1.4

Using the z table to find the Probability

P(z = 1.4) = 83.85%

Therefore, the level of the confidence interval (4.185, 4.215) is 83.85%

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.