Respuesta :
Answer:
The Probability that commute will be between 33 and 35 minutes to the nearest tenth = 0.0189 ≅1.89%
Step-by-step explanation:
Step(i):-
Given mean of the Population(μ) = 41 minutes
Given standard deviation of the Population (σ) = 3 minutes
let 'X' be the random variable of Normal distribution
Let X = 33
[tex]Z = \frac{x -mean}{S.D} =\frac{33-41}{3} = -2.66[/tex]
let X = 35
[tex]Z = \frac{x -mean}{S.D} =\frac{35-41}{3} = -2[/tex]
Step(ii):-
The Probability that commute will be between 33 and 35 minutes to the nearest tenth
P(33≤ X≤35) = P(-2.66 ≤X≤-2)
= P( X≤-2) - P(X≤-2.66)
= 0.5 - A(-2) - (0.5 - A(-2.66)
= 0.5 -0.4772 - (0.5 -0.4961) (From normal table)
= 0.5 -0.4772 - 0.5 +0.4961
= 0.4961 - 0.4772
= 0.0189
The Probability that commute will be between 33 and 35 minutes to the nearest tenth = 0.0189 ≅1.89%
