Question

The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.2 years and a standard deviation of 0.5 years. Using the expanded empirical rule, what is the probability in decimal form that a randomly chosen battery will

(a) last fewer than 3.535 years?
Answer:

(b) last between 2.7 and 3.7 years?
Answer:

(c) last more than 1.7 years?
Answer:

Answer 1

Solution :

Given that,

mean = = 3.2

standard deviation = = 0.5

a ) P( x < 3.535 )

P ( x - / ) < ( 3.535 - 3.2 /0.5)

P ( z < 0.335 / 0.5 )

P ( z < 0.67)

= 0.7486

Probability = 0.7486

b ) P (2.7 < x < 3.7)

P ( 2.7 - 3.2 / 0.5) < ( x -  / ) < ( 3.7 - 3.2 / 0.5 )

P ( -0.5 / 0.5 < z < 0.5 / 0.5 )

P (-1 < z < 1 )

P ( z < 1 ) - P ( z < -1)

Using z table

= 0.8413 - 0.1587

= 0.6826

Probability = 0.6826

c ) P (x > 1-7 )

= 1 - P (x <1-7 )

= 1 - P ( x -  / ) < ( 1-7 - 3.2 / 0.5)

= 1 - P ( z < -1.5 / 0.5 )

= 1 - P ( z < -3 )

Using z table

= 1 - 0.0013

= 0.0013

Probability = 0.0013