Question

Given that a sample is approximately normal with a mean of 25 and a standard deviation of 2, the approximate percentage of observation that falls between 19 and 31 is:

                     i.   67%

                     ii. 75%

                     iii. 95%

                     iv. 99.7%

                     v. can’t be determined with the information given

e.    The Law of Large Numbers implies the following:

               i. To calculate a probability an experiment needs to be theoretically                                                              

                           repeated

                     ii.   Probabilities can be calculated on sampling distributions

                     iii. The Law does not apply to subjective probabilities

                     iv. All of the above

                     v.   None of the above

Answer 1

Question 1

A sample is approximately normal with mean 25, and standard deviation of 2.

We have to find the approximate percentage of observation, that falls between 19 and 31.

Now, 19 is 25-3*2, ie. 3 standard deviations to the left of mean.

And 31 is 25+3*2, ie. 3 standard deviations to the right of mean.

So, we have to find the percentage of the distribution that lies between 3 standard deviations of the mean.

According to the emperical law of normal distribution, we know that 99.73% of the distribution lies between 3 standard deviations of the mean.

So, the correct answer is option (iv) 99.7%.

Question 2

The law of large number states that when the number of experiment increases, the sampling distribution reflects the population distribution, with more and more confoidence.

Now, subjective probability is not based on any formal calculations; it is intuitive, which means law of large numbers can not be applied.

So, to calculate a probability, an experiment needs to be theoretically repeated.

Probabilities can be calculated on sampling distributions.

The law does not apply to subjective probabilities.

All these statements are correct.

So, the correct answer is option (iv) All of the above.