Question

Historically, weights of polar bears have been known to be Normally Distributed with a population mean of approx. 550 kg and a standard deviation of about 110 kg. Researchers are studying the effect of climate change on these animals; their hypothesis is that, because of the diminishing size of their feeding habitats, the average polar bear will be smaller than in the past.

1.) What is the probability that a randomly selected polar bear would weigh less than 480 kg? Would this be an unusual event?

2.) Suppose researchers plan to take a random sample of 20 polar bears and calculate their sample mean. Would this sample mean be the same with every sample? Why or why not? Describe the sampling distribution of the sample mean weight, being sure to address the issue of Center, Shape, and Spread.

3.) What is the probability that a random sample of 20 polar bears would have a mean weight of 500 kg or less? Would this be an unusual event- that is, if we got a sample mean of 500 kg or less, would this be rare or would it be relatively commonplace?

Answer 1

Justifications for 2.:

The sample means would vary from sample to sample and you could plot their distribution with a histogram. We call this distribution the sampling distribution. We call it sampl-ing because it is the distribution from “sampl-ing” lots of times. This is different to the “sample” distribution which is the distribution of the observed data.

An event is said unusual if the probability of occurance of the event is very low(generally,value less than 0.05 are considered unusual).

1) is not unusual as probability is nearly 0.3(low probability but not unusual)

3) is unusual since the probability value is less than 0.05.

If there is any understanding problem regarding this please feel free to ask any doubt in comment box. Thank you