Sampling Distribution of the Sample Mean (Examples)

  1. Suppose the amount of spaghetti sauce in glass jars has a normal distribution with a mean of 850 g and a standard deviation of 12 grams.
    1. What is the probability that a randomly selected jar contains more than 860g of sauce?
    2. What is the probability that a sample of 9 jars has a mean of more than 860 grams of sauce?

  2. Suppose returns from investments have a mean of 7% with a standard deviation of 2%.
    1. What is the probability that 25 investors have an average return of more than 8%?
    2. Assume the information in this problem came from your broker. What assumption would you make if a random sample of 25 investors yielded a mean return of more than 8%?

  3. A weather report claims the mean high temperature during the summer in Columbia, SC is 90 degrees (F). Suppose the standard deviation is known to be 3 degrees (F).
    1. Do you believe the report if a sample of 30 temperatures during the summer yields an average of 91.4 degrees?
    2. What is your opinion if the sample of 30 temperatures yields an average of no more than 89.5 degrees?

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