In-Class Exercise CLT and Sampling Distribution of the Sample Mean

1.   The first histogram below show the distribution of a population. Which of the following three histograms, A, B, or C best portrays the sampling distribution of the mean of a simple random sample of 36?

2.   The breaking strength of steel bars is normally distributed with a mean of 260 pounds per square inch and a standard deviation of 18 psi.

      a.   What is the probability that a single randomly selected steel bar will have a breaking strength greater than 250?

      b.   A shipment of steel bars will be accepted if the mean breaking strength of a random sample of 10 bars is greater than 250 psi. What is the probability that a shipment will be accepted?

      c.   A shipment of steel bars will be accepted if the mean breaking strength of a random sample of 25 bars is greater than 250 psi. What is the probability that a shipment will be accepted?

      d.   If you took many, many samples of 25 bars, approximately 95% of the bars would have sample means between ____________ and ____________.

      e.   If you took many, many samples of 100 bars, approximately 95% of the bars would have sample means between ____________ and ____________.