Question

"Sysnic" battery have had a life expectency of 115 hours. A sample of 49 batteries showed an average life of 118.5 hours. From past information, it is known that population standard deviation of the batteries is 6 hours, and that the life expectency of batteries follow normal distribution.

- If nothing has been changed in a life expectancy of all battteries, what is the probability that sample mean of 49 show average life of 118.5 hours or longer?

Answer 1

Given,

Sample mean, = 118.5 hours

Population standard deviation, = 6 hours

Sample size, n = 49

According to Central Limit Theorem, the distribution of sample mean will be approximately normal with mean of sample mean, = = 118.5 hours and standard error, =

=

= 0.857 hours

P(< A) = P(Z < (A - )/)

P(average life of 118.5 hours or longer) = P( > 118.5)

= 1 - P( < 118.5)

= 1 - P(Z < (118.5 - 118.5)/0.857)

= 1 - P(Z < 0)

= 1 - 0.5000

= 0.5000