A manufacturing firm quality assures components manufactured and historically the length of a tube is found to be normally distributed with a population mean of 100 cm and a population standard deviation of 5 cm.

Calculate the probability that a random sample of one tube will have a length of at least 110 cm.

From the information provided we define X has the tube length in centimetres and population mean μ = 100 and standard deviation σ = 5. This can be represented using the notation X ~ N (100, 5²).

The problem we have to solve is to calculate the probability that 1 tube will have a length of at least 110 cm.

This can be written as P(X ≥ 110) and is represented by the shaded area illustrated in Figure 4.2.

This problem can be solved by using the Excel function NORM.DIST (X, μ, σ², TRUE). This function calculates the area illustrated in Figure 4.3.

Transcribed Image Text:

Normal curve f(x) μ = 100 110 X Figure 4.2