Do you want to own your own candy store? Wowl With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a randon sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution. 96 176 133 92 75 94 116 100 85 A USE SALT (a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost i and sample standard deviation s. (Round your answers four decimal places.) thousand dollars thousand dollars (b) Find a 90% confidence interval for the population average startup costs for candy store franchises. (Round your answers to one decimal place.) lower limit thousand dollars upper limit thousand dollars
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!
The confidence interval gives a range of values for the unknown parameter of the population. The width of the confidence interval increases with an increase in the confidence level.
t distribution is a distribution similar to normal distribution but having heaver tails. t distribution is used when the population standard deviation is unknown or the sample size is less than 30.
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