Answer:
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%
