Answer:
a) P=0.191
b) E(T)=0.2090
c) V(T)= 0.00001102
Step-by-step explanation:
The thickness T is a random variable uniformly distributed between 0.2032 and 0.2147.
a) Determine the proportion of wafers that exceeds 0.2125 micrometers of photoresist thickness.
The proportion is equal to the probability of T>0.2125.
[tex]P(T>0.2125)=1-\frac{T-T_{min}}{T_{max}-T_{min}} =1-\frac{0.2125-0.2032}{0.2147-0.2032} =1-\frac{0.0093}{0.0115} =1-0.809=0.191[/tex]
b) Determine the mean of X (in micrometers)
The mean of a random variable with a uniform distribution is:
[tex]E(T)=0.5(T_{min}+T_{max})=0.5*(0.2032+0.2147)=0.5*0.4179=0.2090[/tex]
c) Determine the variance of X
The variance of a random variable with a uniform distribution is:
[tex]V(T)=\frac{(T_{max}-T_{min})^2}{12} =\frac{(0.2147-0.2032)^2}{12}=\frac{0.0115^2}{12}=\frac{0.00013225}{12} = 0.00001102[/tex]