Problem 10-1 Specifications for a part for a DVD player state that the part shou

Question

Problem 10-1 Specifications for a part for a DVD player state that the part should weigh between 24.5 and 25.5 ounces. The process that produces the parts has a mean of 25.0 ounces and a standard deviation of .25 ounce. The distribution of output is normal. Use Table-A.    
a. What percentage of parts will not meet the weight specs? (Round your "z" value and final answer to 2 decimal places. Omit the "%" sign in your response.)     
  Percentage of parts %       
b. Within what values will 99.74 percent of sample means of this process fall, if samples of n = 8 are taken and the process is in control (random)? (Round your answers to 2 decimal places.)     
  Lower value ,  Upper value  

Please explain step-by-step for solution. Problem 10-1 Specifications for a part for a DVD player state that the part should weigh between 24.5 and 25.5 ounces. The process that produces the parts has a mean of 25.0 ounces and a standard deviation of .25 ounce. The distribution of output is normal. Use Table-A.    
a. What percentage of parts will not meet the weight specs? (Round your "z" value and final answer to 2 decimal places. Omit the "%" sign in your response.)     
  Percentage of parts %       
b. Within what values will 99.74 percent of sample means of this process fall, if samples of n = 8 are taken and the process is in control (random)? (Round your answers to 2 decimal places.)     
  Lower value ,  Upper value  

Specifications for a part for a DVD player state that the part should weigh between 24.5 and 25.5 ounces. The process that produces the parts has a mean of 25.0 ounces and a standard deviation of .25 ounce. The distribution of output is normal. Use Table-A. What percentage of parts will not meet the weight specs? (Round your "z" value and final answer to 2 decimal places. Omit the "%" sign in your response.) Within what values will 99.74 percent of sample means of this process fall, if samples of n = 8 are taken and the process is in control (random)? (Round your answers to 2 decimal places.) Please explain step-by-step for solution. Specifications for a part for a DVD player state that the part should weigh between 24.5 and 25.5 ounces. The process that produces the parts has a mean of 25.0 ounces and a standard deviation of .25 ounce. The distribution of output is normal. Use Table-A. Specifications for a part for a DVD player state that the part should weigh between 24.5 and 25.5 ounces. The process that produces the parts has a mean of 25.0 ounces and a standard deviation of .25 ounce. The distribution of output is normal. Use Table-A. What percentage of parts will not meet the weight specs? (Round your "z" value and final answer to 2 decimal places. Omit the "%" sign in your response.) Within what values will 99.74 percent of sample means of this process fall, if samples of n = 8 are taken and the process is in control (random)? (Round your answers to 2 decimal places.)

Explanation / Answer

you need to find your critical values (z) first:

z=(sample - population mean)/standard deviation

Which here means

z1= (24 - 24.5)/.2 = -2.5

z2= (25- 24.5)/.2 = 2.5

this means you dvd players will fall within plus or minus 2.5 standard deviations away from the mean.

Now using either a z-table in you book or you handy dandy ti-calculator you find the probability.

For the calculator:

P(meeting specs) = normalcdf(-2.5,2.5) <----- [2nd] [distr] [normalcdf]

you want P(of not meeting specs) so do 1-Ans

P(not meeting specs) = .0124

For Part B:

95.44% should be a number you have devoted to memory. It means within 2 standard deviation of the mean.

using the equation from before:

2=(x-24.5)/.2

x=24.9

-2=(x-24.5)/.2

x=24.1

therefore your values wall fall in the range of [24.1,24.9]

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