The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.56 inches and a standard deviation of 0.04 inch. A random sample of 12 tennis balls is selected. Complete parts (a) through (d) below. a. What is the sampling distribution of the mean? O A. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 12 cannot be found. O B. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 12 will not be approximately normal. c. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 12 will also be approximately normal. O D. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 12 will be the uniform distribution. b. What is the probability that the sample mean is less than 2.54 inches? PÃ<2.54) =D (Round to four decimal places as needed.)

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!