Statistics II
Exercises Lesson 0
1. A company is estimating the costs to complete a project, that are divided into two groups: a fixed
cost of 48000 euros and a variable cost of 6500 euros per month of project duration.
The duration of the project is not known in advance, but the company estimates that it may vary
between 3 and 6 months, with probabilities given in the following table:
Duration (D) 3 4 5 6
Probability 0.2 0.3 0.25 0.25
Calculate:
a) The probability function for the total cost of the project.
b) The expected value of the total cost.
c) Its variance and standard deviation.
d) The probability that the cost will exceed 80000 euros
2. A company makes nuts and bolts that are sold in packages with a number of nuts and bolts in each
package that follows the distribution given in the table below:
Number (N) 98 99 100 101 102
Probability 0.1 0.2 0.4 0.15 0.15
Calculate:
a) The probability that a package contains less than 100 nuts and bolts.
b) If two packages are selected randomly, which is the probability that at least one of them will
contain less than 100 nuts and bolts?
c) Compute the mean and the standard deviation for the number of nuts and bolts in a package.
d) If manufacturing one package has a fixed cost of 0,4 euros and a variable cost of 0,005 euros
per each nut and bolt, and the sales price is 1,2 euros, which is the expected value for the
profit of selling one package? And its standard deviation?
3. The demand for a given product the coming month can be approximated as a normal random
variable with mean 850 units and standard deviation equal to 75 units.
Calculate:
a) The probability that the demand during the coming month will be less than 800 units.
b) The probability that the demand will be a value between 825 and 925 units.
c) If the unit profit for each unit sold is 2 euros and the number of units sold is equal to the
demand, which is the expected value of the total profit? What is the variance of the total
profit?
d) What is the probability that the total profit will exceed 1500 euros?
e) Which is the value of the total profit that has a probability of being exceeded equal to 10 %?
4. A company purchases a commodity from two suppliers. The level of defective product in the deli-
veries from both suppliers is assumed to follow normal distributions with parameteres gien in the
following table:
Mean Variance
Supplier 1 4,6 0,49
Supplier 2 5,1 0,16
1
