For each problem identify the sampling distribution explicitlyusing the Central Limit Theorem, use probability notation toindicate what you are being asked to find, find your probabilitiesshowing all your work, including diagrams. Interpret your finalresults. 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 wasselected. Â Â
What is the probability that 36 or more people in this sample,text while driving? Hint: you will need to find the sampleproportion of the 36 adults.
Assume that 15% of the parts produced in an assemblylineoperation are defective, but that the firm’s production manager isnot aware of the situation. Assume further that the qualityassurance department tested 50 parts to determine the quality ofthe assembly operation. If tests show the sampleproportion ofdefective parts is 10% or more, the assemblyline must be shutdown.
Using the above information, what is the probability that theassembly line will need to be shut down?
The average lifetime of a light bulb is 3,000 hours with astandard deviation of 696 hours. A simple random sample of 36 bulbsis taken.
What is the probability that the average life in the samplewill be between 2,670.56 and 2,809.76 hours?
b. What is the probability that the average life in the samplewill be greater than 3,219.24 hours?
c. What is the probability that the average life in the samplewill be less than 3,180.96 hours?
