Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a standard deviation of 1500 hours and a mean life span of 15,000 hours. If a monitor is selected at random, find the probability that the life span of the monitor will be more than 15,884 hours. Round your answer to four decimal places.

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muhammadtalhashoaib muhammadtalhashoaib · Answer 1 · 2019-11-06T11:05:02+01:00

Answer:

0.2776

Explanation:

Mean = 15000, SD = 1500

We need to find Cumulative probability: P(X > 15884)

First we need to convert it into normal distribution.

From the attached file, we can see the shaded area we are looking for.

For conversion as follow; [tex]P (X>15884) =P ( X - mean > 15884-15000 ) =P (\frac{X- mean}{SD} > \frac{15884-15000}{1500} )[/tex]

Next to find Z = [tex]\frac{X- mean}{SD}[/tex] = 0.59

now we have converted to normal distribution and found the value of Z, we need to find the probability P(X > 15884).

P(X > 15884) = P(Z > 0.59).

From the normal distribution table at Z= 0.59, and greater than 0.59, Probability = 0.2776.