Answer:
Step-by-step explanation:
Using normal distribution,
z = (x - μ)/σ
μ= mean = 44 and
σ = standard deviation= 5.0
a) The probability that yield strength is at most 40=
P( x lesser than or equal to 40)
z = (40-44)/5= -0.8
Looking at the normal distribution table,
P( x lesser than or equal to 40) =0.2119
b) P(x greater than 62) = 1 - P(x lesser than or equal to 62)
z = (62-44)/5= 3.6
Looking at the normal distribution table,
P(x greater than 62) = 1 -0.99984
= 0.00016
c)P( 42 lesser than or equal to x lesser than or equal to 62)
= P(x lesser than or equal to 62) - P( x lesser than or equal to 40)
= 0.99987-0.2119= 0.78797
d) What yield strength value separates the strongest 75% from the others.
To get x for strongest 75, we get the z value corresponding to 0.75 from the table
z = 0.675= (x-44)/5
x = 3.375+44 = 47.375
The rest is 25% = 0.25
we get the z value corresponding to 0.25 from the table)
z = -0.67 = (x-44)/5
-3.35= x -44
x = -44+3.35= 40.65
yield strength value that separates the strongest 75% from the others
=47.375-40.65= 6.725
