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!

the answer to the expression is 83