The quality control manager of a light bulb factory needs to estimate the average life of a large shipment of light bulbs. The process standard deviation is known to be 100 hours. A random sample of 64 light bulbs indicated a sample average life of 350 hours. Given the confidence interval calculated above. do you think the manufacturer has the right to state that the light bulbs last on average 400 hours? a. No.
b. Yes.
c. Maybe.
d. Do not know

Complete Question

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours

A. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment.

B. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 400

a. No.

b. Yes.

c. Maybe.

d. Do not know

A

B

  correct option is  a

Step-by-step explanation:

From the question we are told that

   The  standard deviation is  

    The  sample mean is  

      The sample  size is  

Given that the confidence level is  95%  then the level of significance is mathematically represented as

The critical value  of   from the normal distribution table  is  

Generally the margin of error is mathematically represented as

=>    

=>    

Generally the 95% confidence interval is mathematically represented as

This 95% confidence interval  can be interpreted as follows

   There is 95 confidence that the true population mean lies in this interval

 Now  looking at the interval we see that it dose not contain 400 hence

the correct answer is  No the   manufacturer do not  have  the right to state that the light bulbs last on average 400 hours

the answer is ! ?

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.