A type of capacitor has resistance that varies according to

A type of capacitor has resistance that varies according to a normal distribution with a mean of 800 mega ohms and a standard deviation of 200 mega ohms. A certain application specifies capacitors with resistances between 900 and 1,000 mega ohms.

A.What proportion of these capacitors meets this specification?

B.If three capacitors are randomly selected from a lot of capacitors, what is the probability that at least 1 capacitor will meet the criteria?

Solution

a)here we have to find the proprtion of P(900<=X<=1000)

Find the zscore

P(900-800)/200<=x<(1000-800/200)) =>P(.5<=z<=1)

from the z table =>P(z<=1)-P(z<=.5) =>.8413-.6915 =.1498

b)Using binomial distribution

probability of at least 1 capacitor=1-P(X<=1)

                                                   1-3c1 (.1498)^1 *(1-.1498)^2

                        1-3*.1498*.8502^3

                         =>1-3*.614*.1498

                        =.7238 is the required probability