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The shelf life of a battery produced by one major company is known to have a mean life of 5 years and a standard deviation of 0.1 years. What value of shelf life do 16% of the battery shelf lives fall below? Round your answer to one decimal place.

Respuesta :

Answer:

Thus 16% of batteries fall below a life of 4.9 years.(Answer rounded to 1 decimal place)

Step-by-step explanation:

Taking normal distribution of shelf life we have

Given that mean life = 5 years

standard deviation = 0.1 years

Thus standard deviate factor 'Z' corresponding to an area of 16% = -0.994

thus we have

[tex]Z=\frac{X-\bar{X}}{\sigma }[/tex]

Applying values we get

[tex]-0.994=\frac{X-5}{0.1}\\\\\therefore X=5-0.994\times 0.1=4.90065[/tex]

Thus 16% of batteries fall below a life of 4.9 years.  

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