PLEASE HELP!! The batteries from a certain manufacturer have a mean lifetime of 860 hours, with a standard deviation of 70 hours. Assuming that the lifetimes are normally
distributed, complete the following statements.
(a) Approximately of the batteries have lifetimes between 790 hours and
930 hours.
Example
(b) Approximately 95% of the batteries have lifetimes between hours and
hours.

A) 99.74%

B) 633.6 hours and 986.4 hours

Step-by-step explanation:

Solution :

Given that ,

mean =  u =810

standard deviation = sigma  = 90    

P(540< x <1080 ) = P[(540-810) /90 < (x - u   ) /  sigma < (1080-810) /90 )]

= P( -3< Z < 3)

= P(Z <3 ) - P(Z < -3)

Using z table    

=0.9987-0.0013

= 0.9974

answer=99.74%

(B)

middle 95% of score is

P(-z < Z < z) = 0.95

P(Z < z) - P(Z < -z) = 0.95

2 P(Z < z) - 1 = 0.95

2 P(Z < z) = 1 + 0. 95= 1.95

P(Z < z) = 1.95/ 2 = 0.975

P(Z <1.96 ) = 0.975

z  ±1.96    

Using z-score formula  

x= z * sigma  +  u

x= -1.96* 90+810

x= 633.6

Using z-score formula  

x= z * sigma  +  u

x=1.96* 90+810

x= 986.4

633.6 hours and 986.4 hours

depends on how many days you are talking about

step-by-step explanation:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is