The shape of the normal random variable is determined by the mean μ and the standard deviation σ of the distribution.

Mode is the most frequent value in the entire data. The correct answer is D.

In a study about college students, students are classified according to their department and preference of language course. If there are 10 different departments and 5 different language courses, in how many different ways can a student be classified? According to the basic principle of counting, it follows that there are in total 10.5=50 different possible classifications.

In a study about employess, employees are classified according to the department they work in and their preference of training courses. If there are 12 different departments and 7 different courses, according to the basic principle of counting, itf ollows that there are in total 12.7=84 different possible classifications.

The area under the probability density function f (x) is always equivalent to 1

The variance is equal to V (X) = E (X²) - [E (X)]² for f(x) = x for 0 ? x ? 4 the f(x²)=x² which would indicate that x*x² is the function to take the integral in order to find the variance. The integral of x³ is x⁴/4 on 0 ? x ? 4 would yield to the difference of the value found from x = 4 and x = 0. For x=4 the value is 64 and for x=0 the value is 0. The difference between these values is 64. The answer is E.

0,5

arithmetic mean : m = 70 / 5 = 14 ; s = (4 + 2 + 2 + 2 + 6) / 5 = 16 / 5 = 3.2 ; . pg. 112. Correct answer is A.

What information can we obtain from a box plot? The central tendency measure of the distribution is indicated by the median line in the box plot. A measure of the variability of the observations is given by the length of the box. Also, by examining the relative location of the median line, we can obtain about the information of the distribution shape. The correct answer is E. 

In probability, if the occurrence of one event dictates that none of the other events can occur at the same time, we call this event mutually exclusive events.

For X which is a continuous random variable that is uniformly distributed and takes values between 3 and 9, the minimum value of the random variable X is 3 (it’s the value of a) and the maximum value is 9 (it’s the value of b). Then X~U (a=3, b=9) and the probability density function of the continuous random variable X is defined as, f (x) = 1/(b − a) = 1/(9 − 3)= 1/6 for 3≤x≤9. The answer is B.

According to the Bayes's Theorem P(B|A) is equal to [P(A|B)*P(B)]/P(A). The values are given as so P(A|B)=0.30, P(B)=0.25 and P(A)=0.15. P(B|A)=(0.30*0.25)/(0.15) = 0.5. The answer is E.

Here, it is natural to assume that a failure of a mobile phone is independent from a failure of another mobile phone. Therefore, if Ai(i=1,2,3,4) denotes the event that the i-th mobile phone will work without any problem for at least 2 years, then the probability is given by 

P(A1+A2+A3+A4) = P(A1)P(A2)P(A3)P(A4) = (0.90).

The correct answer is B.

Using the same idea, we can try another example, what is the probability of obtaining a number more than 4 if we throw a six-sided fair die? Remember on a six-sided fair die, all the outcomes have the same chance to appear, in this example the question makes a restriction of observing values more than 4. ere are only two outcomes to satisfy this restriction; those are the numbers 5, and 6; therefore, the probability we are looking for is

P(Morethan 4) = 2/6 = 1/3 = 0.333

The correct answer is C.