Question

battery life follows a normal continuous probability distribution with a population mean = 300 hours and a population standard deviation of 30 hours. What is probability that a battery tested will last for less than 270 hours?

What is probability that a battery tested will last between 270 and 330 hours?

The weakest 10% of the population will not exceed what battery life?

Answer 1

Solution :

Given that ,

a) P(x < 270)

= P[(x - ) / < (270 - 300) / 30]

= P(z < -1.00 )

Using z table,

= 0.1587

b) P( 270 < x < 330) = P[(270 - 300)/ 30 ) < (x - ) /  < (330 - 300) / 30 ) ]

= P(-1.00 < z < 1.00 )

= P(z < 1.00) - P(z < -1.00)

Using z table,

= 0.8413 - 0.1587

= 0.6826

c) Using standard normal table,

P(Z < z) = 10%

= P(Z < z ) = 0.10

= P(Z < -1.28 ) = 0.10

z = -1.28

Using z-score formula,

x = z * +

x = -1.28 * 30 + 300

x = 261.6 hours