Answer to Question #237535 in Statistics and Probability for Jack937

Question

The life length of an electric device (a) is normally distributed with mean 45 and standard deviation of 8 while that of a similar electric device (b) has a mean life length 48 and standard deviation of 4. All measurement been in two hours which of the electric device is to prepare for

(1) 48 hours period

(2) 52 hours period

Given the reason for your answer

Answer 1

The 68-95-99.7 rule, provides a quick estimate of the spread of data in a normal distribution given the mean and standard deviation. Specifically, the empirical rule states that for a normal distribution:

68% of the data will fall within one standard deviation of the mean.

95% of the data will fall within two standard deviations of the mean.

Almost all (99.7%) of the data will fall within three standard deviations of the mean.

$\mu_1=45\ hr, \sigma_1=8\ hr$

$\mu_2=52\ hr, \sigma_2=48\ hr$

$\mu_1-1\sigma_1=45-8=37, \mu_1+1\sigma_1=45+8=53$

$\mu_2-1\sigma_2=48-4=44, \mu_2+1\sigma_2=48+4=52$

(1) Both electric devices are o prepare for 48 hours period.

(2) Both electric devices are o prepare for 52 hours period.