STA 112 QUESTIONS FOR QUIZ-TYPE D
1. \( \qquad \) is an arrangement of objects in a definite order.
(a) combination (b)
(b) permutation (c)
2. In how many ways can you choose 3 students from a group of 7 ?
(a) 35
(b) 210
(c) 120
(d) 105
(e) 60
3. How many 3 -digit numbers can be formed using the digits \( 1,2,3,4 \) without repetition?
(a) 12
(b) 24 (c) 64
(d) 60 (e) 72
\begin{tabular}{|l|l|l|l|l|}
\hline X & 0 & 1 & 2 & 3 \\
\hline \( \mathrm{P}(\mathrm{X}=\mathrm{x}) \) & 0.2 & 0.3 & 0.4 & 0.1 \\
\hline
\end{tabular}
4. using the data above, calculate the average time a customer used the system
(a) 49
(b) 64
(c) 1.4
(d) 32
(e) 2.8
5. Using the same data above, calculate the variance
(a) 1.4
(b) 6.4
(c) 1.8
(d) 0.84
(e) 0.32
6. A random variable has the pdf given as \( \mathrm{f}(\mathrm{x})=2 \mathrm{x} \quad 0<\mathrm{x}<1 \). Obtain \( \mathrm{P}(\mathrm{x} \leq 0.4) \)
(a) 0.4
(b) 0.16
(c) 1.4
(d) 0.2
(e) 0.10
7. Which of the following is a property of a binomial distribution?
a) Trials must be dependent (b) Each trial has more than two outcomes (c) Probability of success remains constant (d) The number of trials is not fixed. (e) None
8. If \( \lambda=4 \), what is the mean of the Poisson distribution?
(a) 2 (b) 4 (c) 16 (d) \( \sqrt{ } 4 \) (e) \( 1 / 4 \)
9. The variance of a binomial distribution is given by:
(a) \( n p^{2} \) (b) \( n p(1-p) \) (c) \( n^{2} p \) (d) \( p / n \) (e) \( n^{2} p^{2} \)
10. In a binomial distribution, the expected value (mean) is:
(a) \( n p(1-p) \) (b) \( n p(\mathrm{c}) n+p \)
(d) \( \mathrm{p}(1-\mathrm{p})(\mathrm{e}) \mathrm{pq}(\mathrm{n}-1) \)
11. What is the probability of getting a head when a fair coin is tossed once?
(a) 1 (b) 0 (c) 0.5
(d) 0.25
(e) 0.2
12. If the probability of an event occurring is 0.65 , what is the probability that it does not occur?
(a) 0.35
(b) 0.65
(c) 1.65
(d) 0.45
(e) 0.33
13. In how many ways can 3 boys and 2 girls be selected from a group of 5 boys and 4 girls?
(a) 40
(b) 60
(c) 80
(d) 100 (e) 24
14. If two events \( A \) and \( B \) are mutually exclusive, then
(a)
\[
\begin{array}{l}
P(A \cap B)=P(A)+P(B)(b) P(A \cap B)=0 \\
(e) P(A \cup B)=P(A)+P(B)-P(A \cap B)
\end{array}
\]
(c) \( \mathrm{P}(\mathrm{A} \cup \mathrm{B})=1 \)
(d) \( P(A \cap B)=P(A)-P(B) \)
15. What is the probability of getting a 5 or 6 on a fair die?
(a) \( 2 / 6 \)
(b) \( 1 / 3 \)
(c) \( 1 / 6 \)
(d) Both A and B (e) \( 5 / 6 \)