The amount of calories in a slice of cheese pizza follows a Normal Distribution with a mean of 264 calories and a standard deviation of 24 calories. For each question sketch a graph of the distribution demonstrating the value you are asked to find. A consumer advocate will randomly samples slices of cheese pizza from 38 different locations and compute the sample mean a. What interval contains the sample mean for 95% of all samples of size 38? b. What is the probability that the sample mean is less than 270 calories?
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!
3. The amount of calories in a slice of cheese pizza follows a
264 calories and a standard deviation of 24 calories. For each question sketch a graph of the
distribution demonstrating the value you are asked to find. A consumer advocate will
randomly samples slices of cheese pizza from 38 different locations and compute the sample
mean
a. What interval contains the sample mean for 95% of all samples of size 38?
b. What is the probability that the sample mean is less than 270 calories?
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