Question

A company makes batteries with an average life span of 300 hours with a standard deviation of 75 hours. Assuming the distribution is approximated by a normal curve fine the probability that the battery will last:(give 4 decimal places for each answer)

a. Less than 250 hours

b. Between 225 and 375 hours

c. More than 400 hours

Answer 1

Solution :

Given that ,

mean = = 300

standard deviation = = 75

(a)

P(x < 250) = P[(x - ) / < (250 - 300) / 75]

= P(z < -0.67)

= 0.2514

(b)

P(225 < x < 375) = P[(225 - 300)/ 75) < (x - ) /  < (375 - 300) / 75) ]

= P(-1 < z < 1)

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

= 0.8413 - 0.1587

= 0.6827

(c)

P(x > 400) = 1 - P(x < 400)

= 1 - P[(x - ) / < (400 - 300) / 75]

= 1 - P(z < 1.33)

= 0.0918