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Answered Same DayDec 21, 2021

Answer To: Description Instructions You may open this assessment multiple times but you may only submit it...

David answered on Dec 21 2021
124 Votes
Note: “^” denotes power.
1) Let X be the no of customers per hour. So X~N(600,200^2).
Let Y=16X, i.e.
Y is the no of customers in 16 hours (1 day).
Now by using results we can see,
E(Y) = 16*E(X) = 9600 and,
V(Y) = (16^2)*V(X) = 3200^2
so, Standard deviation(Y) = 3200.
Moreover,
Y~N(9600, 3200^2).
Now the required probability,
P(Y>10000) = P(


>

); Note that Z=


~N(0,1).
=P(Z>0.125)
=0.4503 ;(From standard normal distribution table)
2) From the given data we can see,
Rate of promotion for female professors =


*100% = 20%
Rate of promotion for male professors =


*100% = 20%
Since both the rates are equal so the university is not gender biased.
3) X~Exponential( ).
So the distribution functions are,
f(X)= 0.5exp(-0.5x); x≥ 0
F(x) =P(X≤x)= exp(-0.5x) ; x ≥ 0
Now required probabilities,
P(X>1) =1-P(X≤1) = exp(-0.5) = 0.60653
P(X>0.4)= exp(-0.5*0.4) =0.81873
P(X<0.5)= 1- exp(-0.5*0.5)=0.2212
4) a) Since the no of outcomes possible in...
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