The Food Marketing Institute shows that 18% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.18 and a sample of 800 households will be selected from the population. Use z-table. a. Calculate 0(P), the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals). b. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion (to 4 decimals)? c. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion for a sample of 1,600 households (to 4 decimals)?
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!
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