A design engineer wants to see if the service life of a halogen headlamp is within control. The service life is normally distributed with a mean of 500 hours and a stastandard deviation of 20 hours. What is the sample mean service life for sample 2

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Complete Question

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Answer:

1

The correct option is C

2

The correct option is C

Step-by-step explanation:

From the table give

  The  sample sample  size is  n  =  4          

Generally the sample mean of the service life for sample 2 is mathematically represented as

         [tex]\= x_2 = \frac{525 + 515 + 505 + 515}{4}[/tex]

       [tex]\= x_2 = 515 \ hours[/tex]

Generally the sample mean of the service life for sample 1 is mathematically represented as

         [tex]\= x_1 = \frac{495 + 500 + 505+ 500}{4}[/tex]

       [tex]\= x_1 = 500 \ hours[/tex]

Generally the sample mean of the service life for sample 3 is mathematically represented as

         [tex]\= x_3 = \frac{470 + 480 + 460+ 470}{4}[/tex]

       [tex]\= x_3 = 470\ hours[/tex]

Generally the mean of the sampling distribution of sample mean is mathematically represented as

           [tex]\mu_{\= x} = \frac{\= x_ 1 +\= x_ 2+\= x_ 3 }{3}[/tex]

=>       [tex]\mu_{\= x} = \frac{500 + 515+470 }{3}[/tex]

=>       [tex]\mu_{\= x} =495 \ hours[/tex]

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