Aconsensus forecastis the average of a large number of individual analysts’ forecasts. suppose the individual forecasts fora particular interest rate are normally distributed with a mean of 5.0 percent and a standard deviation of 1.2 percent asingle analyst is randomly selected. find the probability that his/ her forecast isa at least 3.5 percentb at most 6 percentc between 3.5 percent and 6 percent

a)

And we can find this probability using the z table or excel

b)

And we can find this probability using the z table or excel:

c)

And we can find this probability on this way:

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the interest rate of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the z table or excel

Part b

We are interested on this probability

And we can find this probability using the z table or excel:

Part c

And we can find this probability on this way:

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

she will most likely have 33  

step-by-step explanation:

one that is bigger than 3 1/2