Answer to Question #133253 in Statistics and Probability for Pramod

Question #133253
a certain type of storage battery lasts on average 3 yeras with a standard deviation of 0.5 year.assuming that battery life is normally distributed find the probability that a given battery will lasts less than 2.3 years and between 2.5 years and 3.3 years
1
Expert's answer
2020-09-15T17:25:08-0400

Solution to 1

P(X<2.3)

Find the z-score of x=2.3


Z=(xμ)/σZ= (x-\mu) /\sigma

(2.33)/0.5=1.4(2.3 - 3)/0.5 = -1.4

P(Z<z) can now be obtained from the standard normal table since it follows z~N(0,1)

P(Z<-1.4) = 0.0808



Answer : 0.0808


Solution to 2

P(2.5<X<3.3)

This is given by P(X<3.3) - P(X<2.5)

Obtaining the z-score of 3.3 and 2.5 yields:


(3.33)/0.5=0.6(3.3-3)/0.5 = 0.6(2.53)/0.5=1(2.5 - 3)/0.5 = - 1

respectively.

Now

P(X<3.3)P(X<2.5)P(X<3.3)-P(X<2.5)=P(Z<0.6)P(Z<1)= P(Z<0.6) - P(Z<-1)

From the standard normal table; P(Z<0.6)= 0.7257

P(Z<-1)= 0.1587

Thus: P(2.5<X<3.3) = 0.7257 - 0.1587

= 0.567

Answer : 0.567

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment