39 a If a normal distribution has Mu 30 and Sigma 5 what i

39. a. If a normal distribution has Mu = 30 and Sigma = 5, what is the 91st percentile of the distribution? b. What is the 6th percentile of the distribution? c. The width of a hue etched on an integrated circuit chip is normally distributed with mean 3.000 Mum and standard deviation. 140 What width value separates the widest 10% of all such lines from the other 90%?

Solution

(a)

P(X<c)=0.91

--> P((X-mean)/s <(c-30)/5) =0.91

--> P(Z<(c-30)/5) =0.91

--> (c-30)/5 = 1.34 (from standard normal table)

So c= 30+1.34*5=36.7

-----------------------------------------------------------------------------------------------------------

(b)

P(X<c)=0.91

--> P((X-mean)/s <(c-30)/5) =0.06

--> P(Z<(c-30)/5) =0.06

--> (c-30)/5 = -1.55 (from standard normal table)

So c= 30-1.55*5=22.25

-----------------------------------------------------------------------------------------------------------

(c)

P(X<c)=0.9

--> P(Z<(c-3)/0.14) =0.9

--> (c-3)/0.14 = 1.28 (from standard normal table)

So c= 3+1.28*0.14=3.1792