A company makes auto batteries. They claim that 81% of their LL70 batteries are good for 70 months or longer. Assume that this claim is true. Let p be the proportion in a random sample of 9 such batteries that are good for 70 months or more. a. What is the probability that this sample proportion is within 0.02 of the population proportion? Round your answer to two decimal places. b. What is the probability that this sample proportion is less than the population proportion by 0.05 or more? Round your answer to two decimal places.

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A: Formula :

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.