Base 10 has the ten digits: {0, 1, 2, 3, 4, 5, 6,7, 8, 9}
Base 11 has the digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A} where A is treated as a single digit number
Base 12 has the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B}
Base 13 has the digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C}
Base 14 has the digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D}
The digit D is the largest single digit of that last set. So the largest 3-digit base 14 integer is DDD which is the final answer
Note: It is similar to how 999 is the largest 3-digit base 10 integer
Answer:
a)
And we can find this probability with this difference and with the normal standard table or excel:
b) 
And we can use the z score defined by:

And using the limits we got:


And we want to find this probability:

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 resitances 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 with this difference and with the normal standard table or excel:
Part b
We select a sample size of n =4. And since the distribution for X is normal then we know that the distribution for the sample mean
is given by:
And we want this probability:

And we can use the z score defined by:

And using the limits we got:


And we want to find this probability:
