Question

Chris had heard god things about pilot fountain pens writing well right out of the box. he decides to test this by buying pilot pens until he gets one that does not write well. assume 95% of pilot pens write well right out of the box.

a. how many pens do you expect Chris to buy?

b. what is standard deviation of the number of pens Chris buy?

c. . what is standard deviation of the number of pens Chris buy that write well?

d. what is the probability Chris buys 10 pilot pens?

e. what is the probability that the number of pen Chris buys is an even number that is at least 6?

Answer 1

This is Geometric distribution with parameter

p=probability not write well =1-0.95 =0.05

a)

Mean of distribution=μ=1/p=1/0.05=20

b)

Standard deviation σ-√(1-p)/p=sqrt((1-0.05))/0.05) =19.4936

c)

Standard deviation of number of pens that write well =standard deviation that not write well =19.4936

d)

P(X=10)=P(first 9 write well and 10th not) =(1-0.05)^9*0.05 =0.0315

e)

P(X>=6 and even) =P(X=6)+P(X=8)+P(X=10)+.......

=(0.95)^5*0.05+(0.95)^7*0.05+(0.95)^9*0.05+(0.95)^11*0.05+....

=(0.95)^5*0.05/(1-0.95^2)

=0.3968

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

DEAR STUDENT,

IF YOU HAVE ANY QUERY ASK ME IN THE COMMENT BOX,I AM HERE TO HELPS YOU.PLEASE GIVE ME POSITIVE RATINGS

*****************THANK YOU***************