Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 70 GPa and 2.2 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.) (a) Calculate P (69 ≤ X ≤ 71) when n = 16.

P (69 ≤ X≤ 71) = 0.34728

Step-by-step explanation:

Hello!

Your study variable is X: stiffness of an elastic metal sheet.

X~N (μ; σ²)

To be able to calculate this probability you need to standardize the variable that way you can use the Z-table to get the probabilities for the study variable. The Z-table shows cumulative probabilities P (Z≤z)

P (69 ≤ X≤ 71)

You can rewrite this probability as:

P (X ≤ 71) - P (X ≤ 69)

Now you standardize both terms

P (Z ≤ (71 - 70) / (2.2)) - P (Z ≤ (69 - 70) / (2.2)) = P (Z ≤ 0.45) - P (Z ≤ - 0.45) = 0.67364 - 0.32636 = 0.34728

-i hope you have a nice day!