When Colton commutes to work the amount of time it takes him to arrive is normally distributed with a mean of 41 minutes and a standard deviation of three minutes what percentage of his commute will be between 33 and 35 minutes to the nearest tenth?

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

let X = 35

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%