Respuesta :
Answer:
The proportion of measurements between 25 and 55
P( 25 ≤ X≤ 55) = 0.6826
Step-by-step explanation:
Step(i):-
Given that the mean of the Population = 40
Given that standard deviation of the Population = 15
Let 'x' be the random variable in normal distribution
Let 'X' = 25
[tex]Z = \frac{x-mean}{S.D} = \frac{25-40}{15} = -1[/tex]
Let 'X' = 55
[tex]Z = \frac{x-mean}{S.D} = \frac{55-40}{15} = 1[/tex]
Step(ii):-
The probability that between 25 and 55
P( 25 ≤ X≤ 55) = P( -1≤z≤1)
= A(1) - A(-1)
= A(1) + A(1)
= 2 × A(1)
= 2× 0.3413
= 0.6826
The proportion of measurements between 25 and 55
P( 25 ≤ X≤ 55) = 0.6826
Final answer:-
The proportion of measurements between 25 and 55
P( 25 ≤ X≤ 55) = 0.6826
