With this graph!
the graph shows the normal distribution of the length of similar etc
see attached image

a)68.2%

b)13.6%

Step-by-step explanation:

The question is on continuous probability distributions described by normal equations

You can use the normal distribution calculator in this case

Given that ;

mean is 5 , standard deviation is 0.02 cm

a)To find the probability that the length falls between 4.98 and 5.02

This means

P(4.98<x<5.02) = P(x<5.02)-P(x<4.98)

Find using the normal distribution calculator P(x<4.98) where mean is 5 , standard deviation is 0.02 and normal random variable,x=4.98

P(x<4.98)=0.159

Find using the normal distribution calculator P(x<5.02) where mean is 5, standard deviation is 0.02 and the normal random variable is, x=5.02

P(x<5.02)=0.841

To get;

P(4.98<x<5.02)=P(x<5.02)-P(x<4.98)

P(4.98<x<5.02)=0.841-0.159=0.682

change into percentage

0.682×100=68.2%

b)To find the probability that the length fall between 5.02 and 5.04

This means

P(5.02<x<5.04)=P(x<5.04)-P(x<5.02)

where mean is 5 and standard deviation is 0.02

P(x<5.04)=0.977

P(X<5.02)=0.841

P(5.02<x<5.04)=P(x<5.04)-P(x<5.02)

=0.977-0.841=0.136

change to percentage

0.136×100=13.6%

-232

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is