Question

Battery life follows a normal continuous probability distribution with a population mean = 300 hours and a population standard deviation of 30 hours.

a. What is probability that a battery tested will last for less than 270 hours?

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

Answer 1

Solution :

a.

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

= P(z < -1)

= 0.1587

Probability = 0.1587

b.

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

= P(-1 < z < 1)

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

= 0.8413 - 0.1587

= 0.6826

Probability = 0.6826