Answer:
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!
