Question

$\mu = n \bullet p$
#42 what is the variance (var) for the number of companies that youd expect to fail?
(a) 18.00 (b) 18.25 (c) 18.50 (d) 18.75 (e) none of these
$var = n \bullet p \bullet (1 - p)$
#43 what is the standard deviation (sd) for the number of companies that youd expect to fail? note: please round your answer to three (3) decimal places.
(a) 4.000 (b) 4.250 (c) 4.330 (d) 4.750 (e) none of these
$sd = \sqrt{var}$

• note: a clueless student (not you, of course!) forgot to study for a quiz which contains 15 questions. so, s/he decides to answer every question by just guessing randomly from among five choices: (a) (b) (c) (d) (e) please answer the following 15 questions below about this clueless student.

#44 what type of probability distribution is described by this students strategy?
(a) normal (b) poisson (c) binomial (d) none of these
#45 what is the probability that this student will answer any given question correctly?
(a) 10% (b) 20% (c) 25% (d) 50% (e) none of these
#46 what is the probability that this student will answer any given question incorrectly?
(a) 90% (b) 80% (c) 75% (d) 50% (e) none of these
$\mu = n \bullet p$
#47 what is the expected number ($\mu$) of questions you would expect them to get right?
(a) 1 (b) 2 (c) 3 (d) 4 (e) none of these
$var = n \bullet p \bullet (1 - p)$
#48 what is the variance (var) for the number of questions answered correctly? note: please round your answer to three (3) decimal places.
(a) 1.200 (b) 2.400 (c) 3.200 (d) 3.400 (e) none of these

Explanation:

[44] Identify distribution type

The student guesses 15 independent questions (fixed trials) with 20% correct probability (constant success rate) and two outcomes (correct/incorrect) → Binomial.

[45] Calculate correct probability

Each question has 5 choices, so $p = \frac{1}{5} = 0.2 = 20\%$.

[46] Calculate incorrect probability

$1 - p = 1 - 0.2 = 0.8 = 80\%$.

[47] Compute expected value

$\mu = np = 15 \times 0.2 = 3$.

[48] Compute variance

$VAR = np(1-p) = 15 \times 0.2 \times 0.8 = 2.4$, which is not among options A-D → None of these.

Answer:

[44] C. Binomial
[45] B. 20%
[46] A. 80%
[47] C. 3
[48] E. None of these