Answer to Question #308336 in Statistics and Probability for niks

Question

A certain type of battery has a mean shelf life of 750 with a standard deviation 0f 33 days

a. What is the probability that the shelf life of batteryis below 350 days

b. what is the probability that the shelf life of battery is between 717 and 816 days

Answer 1

$\mu=750,\sigma=33,Z=(x-μ)/σ$

a. $P(x<350)=P(Z<(350-750)/33)=P(Z<-12.12)$

From z distribution tables

$P(Z<-12.12)=0.000$

b. $P(717<x<816)=P((717-750)/33<Z<(816-750)/33)$

$=P(-1<Z<2)=P(Z<2)-P(Z<-1)$

$=0.9772-0.1587$

$=0.8185$