Answer:
P(15.99 ≤ X ≤ 16.01) = 0.1586
Step-by-step explanation:
Explanation:-
Step(i):-
Given data the inside diameter of a randomly selected piston ring is a random variable with mean value 16 cm and standard deviation 0.05 cm.
The mean of the Population 'μ' = 16cm
The standard deviation of the Population 'σ' = 0.05cm
Given 'X' be the Normal Variable
(i) Given X = 15.99
[tex]Z _{1} = \frac{x-mean}{S.D} = \frac{15.99-16}{0.05} = -0.2<0[/tex]
(ii) Given X = 16.01
[tex]Z_{2} = \frac{x-mean}{S.D} = \frac{16.01-16}{0.05} = 0.2>0[/tex]
Step(ii):-
P(x₁ ≤ X ≤ x₂) = A(z₂)+A(z₁)
P(15.99 ≤ X ≤ 16.01)= P(-0.2≤ z ≤ 0.2) = A(z₂)+A(z₁)
= A(0.2)+A(-0.2) [ A(-Z) = A(Z)]
= 0.0793 + 0.0793
= 0.1586
Conclusion:-
P(15.99 ≤ X ≤ 16.01) = 0.1586
