Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a standard deviation of 1200 hours and a mean life span of 18,000 hours. If a monitor is selected at random, find the probability that the life span of the monitor will be more than 16,800 hours. Round your answer to four decimal places.

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JeanaShupp JeanaShupp · Answer 1 · 2019-11-05T06:22:55+01:00

Answer: 0.8413

Step-by-step explanation:

Let x be a random variable that represents the life span of monitors manufactured by TSI Electronics .

Also Monitors manufactured by TSI Electronics have life spans that have a normal distribution with

[tex]\mu=18000[/tex] hours

[tex]\sigma=1200[/tex] hours

∵ [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

Then for x= 16,800 hours,

[tex]z=\dfrac{16800-18000}{1200}=-1[/tex]

The probability that the life span of the monitor will be more than 16,800 hours. :-

[tex]P(x>16800)=P(z>-1)=1-P(z\leq-1)\\\\=1-(1-P(z\leq1)\\\\=P(\leq1)= 0.8413447\approx 0.8413[/tex]

Hence, he probability that the life span of the monitor will be more than 16,800 hours = 0.8413