A cetain type of automobile battery is known to last an aver

A cetain type of automobile battery is known to last an average of 1110 days with a standard deviation of 80 days. Suppose that 400 of these batteries are selected. Find the probability that the average length of life of 400 selected batteries is between 1105 and 1110 Is the probability calculated in (a) exact or approximate? Explain.

Solution

a).

standard error =sd/sqrt(n) = 80/sqrt(400) =80/20 =4

z value for 1105, z=(1105-1110)/4 = -1.25

z value for 1110, z=(1110-1110)/4 = 0

P( 1105<x<1110) = P( -1.25<z<0)

=P( Z < 0 ) – P( z < -1.25)

= 0.5- 0.1056

= 0.3944

b).

The above probability is exact because we use population standard deviation and standard normal distribution to find probabilities.