Answered: uppose that the speed at which cars go…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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uppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and standard deviation 6 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.

b. If one car is randomly chosen, find the probability that it is traveling more than 73 mph.

c. If one of the cars is randomly chosen, find the probability that it is traveling between 70 and 76 mph.

d. 72% of all cars travel at least how fast on the freeway? mph.

PLEASE ANSWE THE 3 SUBS B, C, D

Expert Solution

Step 1

Given Information:

The speed at which cars go on the freeway is normally distributed with mean 71 mph and standard deviation 6 miles per hour.

$μ = 71$ and $σ = 6$

Let X be the speed for a randomly selected car.

(b) If one car is randomly chosen, to find the probability that it is traveling more than 73 mph:

Z-score is a measure which tells how many standard deviations away, a data value is, from the mean. It is given by the formula:

$Z = \frac{X - μ}{σ}$

Required probability is obtained as follows:

$\begin{array}{rcl} P (X > 73) & = & 1 - P (X < 73) \\ = & 1 - P (\frac{X - μ}{σ} < \frac{73 - 71}{6}) \\ = & 1 - P (Z < 0.3333) \\ = & 1 - 0.630546 [U \sin g E x c e l f o r m u l a " = N O R M . S . D I S T (0.3333, T R U E) "] \\ = & 0.369454 \end{array}$

Therefore, probability that it is traveling more than 73 mph is 0.3695

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