Power+, Inc produces AA batteries used in remote controlled toy cars. The mean life of these batteries follows the normal probability with a mean of 37 hours and a standard deviation of 5.5 hours.
As a part of its quality assurance program Power+, Inc. tests sample of 9 batteries
a) What proportion of the sample will have a mean useful life greater than 36.5 hours ?
b) what proportion of the sample will have a mean useful life between 36.5 and 38.5hrs? (Round z value to 2 decimal places and final 4
For sample means you have to divide the standard deviation by the square root of the sample number.
So, the sample standard deviation is 5.5 / √9 = 5.5 / 3 = 1.833
a) Z = 36.5-37 / 1.833 = -0.27
then p(36.5) = 0.3936
b) Z of 38.5 = 38.5-36.5 / 1.833 = 1.09
then p(38.5) = 0.8621
between 36.5 and 38.5 is
0.8621 - 0.3936 = 0.4685
Oh, sorry, correct for a)
they want the proportion GREATER than 36.5
So then it's 1 - 0.3936 = 0.6064
that's the correction for a)
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