Question

A battery manufacturer claims that the lifetime (X) of a certain type of battery is normally distributed with a population mean of 40 hours and standard deviation 10 hours.

(a) If the claim is true, what is P ( X ≤ 36.7 )?

(b) Let X ¯ be the mean lifetime of the batteries in a random sample of size 100.  If the claim is true, what is P ( X ¯ ≤ 36.7 )?

Answer 1

Solution :

Given that,

mean = = 40

standard deviation = = 10   

P ( X ≤ 36.7 )= P[(X- ) / ≤(36.7-40) /10 ]

= P(z ≤ -0.33)

Using z table

probability= 0.3707

B.

n = 100

= 40

=  / n = 10 / 100=1

P(  ≤36.7) = P[( - ) / < (36.7-40) /1 ]

= P(z < -3.3)

Using z table  

=0.0005   

probability= 0.0005