Question

The population mean weight of a one-year old African Penguin is 1585 grams with a standard deviation of 256 grams. If 49 one year old African penguins are selected at random and weighed, what is the probability their mean weight at least 1650 grams? round your answer to three decimal places

Answer 1

We will make use of the central limit theorem.

The population mean =1585, and the standard deviation =256

The random sample is of size: 49.

Let, be the random sample of weights obtained.

Then, . By the central limit theorem, the approximate distribution of is

Let, (The denominator is the standard deviation of ). Then Z~N(0,1), the standard normal distribution.

So, we want the following probability:

Now, I will make use of standard normal distribution calculator or a table to fetch the value of

This gives,

Therefore,

Thus, rounded off to 3 decimal places, is the answer.