For each problem identify the sampling distribution explicitly using the Central Limit Theorem, use probability notation...

For each problem identify the sampling distribution explicitly using the Central Limit Theorem, use probability notation to indicate what you are being asked to find, find your probabilities showing all your work, including diagrams. Interpret your final results. Submit your completed homework to Canvas.

A 2012 survey of adults 18 years and older reported that 34% have texted while driving. A random sample of 125 adults was selected.

What is the probability that 36 or more people in this sample, text while driving? Hint: you will need to find the sample proportion of the 36 adults.

Assume that 15% of the parts produced in an assemblyline operation are defective, but that the firm’s production manager is not aware of the situation. Assume further that the quality assurance department tested 50 parts to determine the quality of the assembly operation. If tests show the sampleproportion of defective parts is 10% or more, the assemblyline must be shut down.

Using the above information, what is the probability that the assembly line will need to be shut down?

The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken.

What is the probability that the average life in the sample will be between 2,670.56 and 2,809.76 hours?

b. What is the probability that the average life in the sample will be greater than 3,219.24 hours?

c. What is the probability that the average life in the sample will be less than 3,180.96 hours?

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