Historically, weights of polar bears have been known to beNormally Distributed with a population mean of approx.550 kg and a standard deviation of about110 kg. Researchers are studying the effect ofclimate change on these animals; their hypothesis is that, becauseof the diminishing size of their feeding habitats, the averagepolar bear will be smaller than in the past.
1.) What is the probability that a randomly selected polar bearwould weigh less than 480 kg? Would this be an unusual event?
2.) Suppose researchers plan to take a random sample of 20 polarbears and calculate their sample mean. Would this sample mean bethe same with every sample? Why or why not? Describe the samplingdistribution of the sample mean weight, being sure to address theissue of Center, Shape, and Spread.
3.) What is the probability that a random sample of 20 polarbears would have a mean weight of 500 kg or less? Would this be anunusual event- that is, if we got a sample mean of 500 kg or less,would this be rare or would it be relatively commonplace?
