Suppose that the speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to two decimal places.

A. X ~ N( , )
B. If one car is randomly chosen, find the probability that is traveling more than 70 mph.
C. If one of the cars is randomly chosen, find the probability that it is traveling between 65 and 75 mph.
D. 90% of all cars travel at least how fast on the freeway? mph.

A)

B) the probability that is traveling more than 70 mph is 0.3446

C) the probability that it is traveling between 65 and 75 mph is 0.6449

D) 90% of all cars travel at least 56.85 mph fast on the freeway

Step-by-step explanation:

The speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 5 miles per hour.

Mean =

Standard deviation =

A) X ~ N( _____, _______ )

In general

So,

B) If one car is randomly chosen, find the probability that is traveling more than 70 mph.i.e.P(X>70)

So,

Z=0.4

Using Z table

P(Z>70)=1-P(Z<70)=1-0.6554=0.3446

Hence the probability that is traveling more than 70 mph is 0.3446

C) If one of the cars is randomly chosen, find the probability that it is traveling between 65 and 75 mph.

P(65<X<75)

AT x = 65

Z=-0.6

AT x = 75

Z=1.4

Using Z table

P(65<X<75)=P(-0.6<Z<1.4)=P(Z<1.4)-P(Z<-0.6)=0.9192-0.2743=0.6449

Hence the probability that it is traveling between 65 and 75 mph is 0.6449

D)90% of all cars travel at least how fast on the freeway?

Since we are supposed to find at least how fast on the freeway

So,P(X>x)=0.9

1-P(X<x)=0.9

1-0.9=P(X<x)

0.1=P(X<x)

Z value at 10% =-2.23

So,

56.85 = x

Hence 90% of all cars travel at least 56.85 mph fast on the freeway

The simplified expression is

20x^2 - 33x - 27

Step-by-step explanation:

(6x - 9 - 2x)(8 + 5x - 5)

We must first rewrite the expression as a product of two binomials.

This can be done by adding like terms

(6x - 9 - 2x)(8 + 5x - 5)

We have,

(4x-9)(5x+3)

Multiplying the resulting binomial expression

(4x-9)(5x+3)

(20x^2+12x-45x-27)

Add the like terms

20x^2-33x-27

The simplified expression is

20x^2 - 33x - 27

Twenty x squared minus thirty-three x minus twenty-seven