Question

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?

Answer 1

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

$Z = \frac{x -mean}{S.D} =\frac{33-41}{3} = -2.66$

let X = 35

$Z = \frac{x -mean}{S.D} =\frac{35-41}{3} = -2$

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%