Answer:
B
Step-by-step explanation:
In this question, we will be calculating the probability between a range using normal distribution.
We proceed as follows;
we have, mean (μ)= 3 and standard deviation (σ) = 1
P(2.5<X<3.5) = P(2.5 - 3 < X- μm < 3.5 -3) = P( -0.5/1 < (X - μ ) /σ < 0.5/1 )
since Z= (X - μ ) / σ
P(2.5<X<3.5) = P(-0.5 < Z < 0.5)
Using Standard Normal Table or Z-calculator it can be found that ,
P(-0.5 < Z < 0.5) = 0.383
because P(−0.5<Z<0.5 ) = P ( Z<0.5 ) − P (Z<−0.5 )
using Standard Normal Table : P ( Z<0.5 )=0.6915 and P ( Z<−0.5 ) can be found by using the following fomula.
P ( Z<−a)=1−P ( Z<a )
After substituting a=0.5 we have: P ( Z<−0.5)=1−P ( Z<0.5 )
We see that P ( Z<0.5 )=0.6915 so,
P ( Z<−0.5)=1−P ( Z<0.5 )=1−0.6915=0.3085
At the end we have: P (−0.5<Z<0.5 )= P ( Z<0.5 ) − P (Z<−0.5 ) = 0.383
