Concept Questions

Please put your answers in the following table.

1	2	3	4	5	6	7	8	9	10

1. Which statement is not true about the mean of a random variable?

A) The mean is the average of all possible values of the random variable.

B) The mean could be estimated by adding up samples of the random variable and then dividing by the number of samples.

C) The mean can be estimated as the middle sample of a sorted set of samples if the number of samples is odd.

D) The mean has the same unit as that of the random variable.

2. Two independent random variables and follow normal distribution with and , respectively. Which statement is true about ?

A) The mean of is 50.

B) The mean of is 40.

C) The standard deviation of is 3.

D) The standard deviation of is 5.

3. The diameter of a rod is measured 10 times and the results are given below.

10.10

10.36

9.54

10.17

10.06

9.73

9.91

10.06

10.71

10.55

The average of the diameter is

A) 17.2 mm

B) 20.5 mm

C) 10.1 mm

D) 20.4 mm

4. For problem 3, the standard deviation of the diameter is

A) 10.2 mm

B) 0.01 mm

C) 0.35 mm

D) 105 mm

5. A bar has a diameter of 10 mm and is subject to a random axial force. If the force is normally distributed, determine the mean and standard deviation of the normal stress developed in the bar.

A) ,

B) ,

C) ,

D) ,

6. For problem 5, what is the probability that the force is less than 18 kN or ?

A) 0

B) 15.87%

C) 84.13%

D) 50%

7. Two aluminum rods with the same diameter of 8.33 mm support the vertical force . Which of the following statements is not true?

A) The average force developed in rod AC is 34.65 kN.

B) The forces developed in AC and AB are dependent.

C) The average force developed in rod AB is 17.31 kN.

D) The standard deviation of the force developed in rod AC is the same as that in rod AB.

8. For the above problem, if the allowable tensile stress for the aluminum is, what is the probability of failure of rod AB? Assume that P and Sa are independent.