I ALWAYS RATE :) A device that monitors the levels of pollutants has sensors tha

Question

I ALWAYS RATE :) A device that monitors the levels of pollutants has sensors that detect the amount of CO in the air. Placed in a particular location, it is known that the amount of CO is normally distributed with a mean of 6.23 ppm and a variance of 4.26 ppm^2. I need to know how to get it because I have the correct answer (Answer to 1 is 0.955 and Answer to 2 is about 5). 1.) A sample of five CO readings is taken. What is the probability that the mean of this sample has a reading less than 7.8 ppm? 2.) The probability that a single random reading of the CO level being between A ppm and 7.8 ppm is 0.50. What is the value of A? (IF YOU JUST PUT THE ANSWER THEN I WILL NOT RATE YOU WELL)

Explanation / Answer

(1) P(xbar<7.8)= P((xbar-mean)/(s/vn) <(7.8-6.23)/(sqrt(4.26/5)))

=P(Z<1.7)

=0.9554 (from standard normal table)

(2) P(A<X<7.8)=0.5

--> P((A-6.23)/sqrt(4.26) <(X-mean)/s <(7.8-6.23)/sqrt(4.26) )=0.5

--> P((A-6.23)/sqrt(4.26)<Z<0.76)=0.5

--> P(Z<0.76)- P(Z<(A-6.23)/sqrt(4.26)) =0.5

--> P(Z<(A-6.23)/sqrt(4.26))=0.7764 -0.5 =0.2764

--> (A-6.23)/sqrt(4.26) =-0.59 (from standard normal table)

--> A =6.23 -0.59*sqrt(4.26) =5.01

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.