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2 answers:
Let 
be the random variable for the part's diameter, and 
the same variable transformed into one that follows the standard normal distribution. You're looking for the proportion of the parts that lie 2 standard deviations away from the mean, which translates to
Recall the empirical rule, which says that approximately 95% of a normal distribution falls within 2 standard deviations of the mean, or
. This means
So out of 15000 parts, you should expect about 5% of them, or about 750 parts to be rejected.
Recall the empirical rule, which says that approximately 95% of a normal distribution falls within 2 standard deviations of the mean, or
So out of 15000 parts, you should expect about 5% of them, or about 750 parts to be rejected.
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Answer:
The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.
Step-by-step explanation:
Dimensions of the rectangle
Height = 5cm
Rate of base = 3/2 cm/min
Area = 60cm^2
We know the area of a rectangle of given by = base* Height
b*h = 60
b*5 = 60
b = 12cm
Applying Pythagoras theorem while drawing a diagonal to the rectangle
so our diagonal will be 13cm
Upon differentiating the area of the rectangle we get
b*h = A=60cm^2
using the chain rule of differentiation
h*db/dt + b*dh/dt = 0
b*dh/dt = -h*db/dt
12*dh/dt = -5*3/2
dh/dt = -5/8 cm//min
so the height of the rectangle is decreasing at the rate of -5/8cm/min
now we have all the measurements we need
b = 12 , db/dt = 3/2cm/min
h = 5 , dh/dt = -5/8 cm/min
Upon differentiating we get
2b*db/dt + 2h*dh/dt = 2D*dD/dt
b*db/dt + h*dh/dt = D*dD/dt
12*3/2 + 5*(-5/8) = 13*dD/dt
18 -25/8 = 13*dD/dt
= 13*dD/dt
dD/dt =
Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.