Question

The class measured the density of a copper block to be 8.6 +/-0.2 g/cm3 at the 95% confidence interval with a standard deviation of 0.4 g/cm. The true density of copper is 8.96 g/cm3.
a. What is the high and low number of the confidence interval range? Does the true value fall within the confidence interval?
high:
low:
within range?
b. What is the high and low of the standard deviation range? Does the true value fall within the standard deviation?
high:
low:
within range?

Answer 1

Answer: kindly check explanation

Explanation:

Given the following :

Measured density of copper block:

8.6+/-0.2 g/cm3

True density = 8.96g/cm3

Standard deviation = 0.4g/cm

a. What is the high and low number of the confidence interval range?

High : 8.6 + 0.2 g/cm3 = 8.8g/cm³

Low : 8.6 - 0.2 g/cm3 = 8.4g/cm³

Does the true value fall within the confidence interval? NO

Actual density = 8.96g/cm³ doses not lie in between (8.4 - 8.8)g/cm³

B.) High and low of the standard deviation range?

High = 8.6 + 0.4 = 9.0g/cm³

Low = 8.6 - 0.4 = 8.2g/cm³

Value falls within range of the true density value of copper block.

8.96g/cm³ falls in-between (8.2-9.0)g/cm³