Back to the Table of Contents
Statistical Probabilities and Distributions
Homework for Prob./Dist. Lesson 10
- Suppose a bank knows that on average 60 customers arrive in a
certain service hour. Using a time interval of 1 minute, calculate
the probability of exactly one customer arriving in a given one
minute interval within that hour. Use the
example in the lecture
for exactly two as a pattern.
- Suppose a bank knows that on average 60 customers arrive in a
certain service hour. Using a time interval of 1 minute, calculate
the probability of no customers arriving in a given one
minute interval within that hour.
- Suppose a bank knows that on average 60 customers arrive in a
certain service hour. Using a time interval of 1 minute, calculate
the probability of exactly three customers arriving in a given one
minute interval within that hour.
- Suppose a bank knows that on average 60 customers arrive in a
certain service hour. Using a time interval of 1 minute, calculate
the probability of more than three customers arriving in a given one
minute interval within that hour.
- Graph the probability distribution determined in the problems
above (and the lecture example).
- Assume a finite population as follows: {1,2,3,4,5,6}.
Note how there are N=6 possible samples of size n=1 and that
each element is its own sample mean. The mean of these sample means
is obviously the population mean.
- Although our samples are too small (n=1) to form a sample standard
deviation, we can calculate the population standard deviation.
- Now calculate the 15 sample means,
without replacement, for all 6C2=15 samples of
size n=2: {{1,2}, {1,3}, {1,4}, ...{5,6}}.
- Once you have the 15 sample means, calculate their mean and standard
deviation.
- Compare this with the mean and standard deviation of the
original population (N=6).
- What is the approximate relationship between the two standard
deviations (or variances)? Should we be using sample or population
standard deviation?