C955 OA WGU – Applied Probability and Statistics 2026 | Objective Assessment (OA) Practice Test – 150 Questions with CORRECT DETAILED 100%ANSWERs & Explanations | Instant Pdf Download

C955 OA WGU – Applied Probability and
Statistics
2026 | Objective Assessment (OA) Practice
Test – 150
Questions with CORRECT DETAILED
100%ANSWERs & Explanations | Instant Pdf
Download

Question 1
A manufacturer produces light bulbs. The probability that a
randomly selected bulb is defective is 0.05. If a quality inspector
selects 10 bulbs at random, what is the probability that exactly 2
bulbs are defective?

A. 0.0746
B. 0.0815
C. 0.0953
D. 0.1029

CORRECT DETAILED 100%ANSWER: A
Explanation: This is a binomial probability problem:

P(X=k)=(nk)pk(1−p)n−kP(X=k) = \binom{n}{k} p^k (1-p)^{n-k}
P(X=k)=(kn
)pk(1−p)n−k P(X=2)=(102)(0.05)2(0.95)8≈0.0746P(X=2) =
\binom{10}{2}
(0.05)^2 (0.95)^8 \approx
0.0746P(X=2)=(210)(0.05)2(0.95)8≈0.0746

Question 2

,The mean of a data set is 50 and the standard deviation is 5.
Using
Chebyshev’s inequality, at least what proportion of the data lies
within 15 units of the mean?

A. 0.75
B. 0.89 C. 0.95
D. 0.97
CORRECT DETAILED 100%ANSWER: B
Explanation: Chebyshev’s inequality:

1−1k21 - \frac{1}{k^2} 1−k21

Here, k=155=3k = \frac{15}{5} = 3k=515=3, so

1−19=0.888≈0.891 - \frac{1}{9} = 0.888 \approx
0.891−91=0.888≈0.89

Question 3
A study finds that the correlation coefficient between study hours
and exam scores is 0.85. Which statement is correct?

A. There is a strong positive linear relationship.
B. There is a weak positive linear relationship.
C. There is a strong negative linear relationship.
D. There is no linear relationship.

CORRECT DETAILED 100%ANSWER: A
Explanation: A correlation of 0.85 indicates a strong positive
linear relationship between the two variables.


Question 4

,In a normal distribution with mean 100 and standard deviation 15,
what is the zscore of a value of 130?

A. 1.50
B. 2.00
C. 2.33
D. 3.00

CORRECT DETAILED 100%ANSWER: A
Explanation: Z-score formula:
z=x−μσ=130−10015=2.0z = \frac{x-\mu}{\sigma} = \frac{130-
100}{15} =
2.0z=σx−μ=15130−100=2.0

Correction: This is actually B. 2.00


Question 5
A continuous random variable X has the probability density
function f(x)=3x2f(x) = 3x^2f(x)=3x2 for 0≤x≤10 \le x \le 10≤x≤1.
What is P(X<0.5)P(X < 0.5)P(X<0.5)?

A. 0.125
B. 0.25
C. 0.375
D. 0.50

CORRECT DETAILED 100%ANSWER: A
Explanation: Integrate the pdf from 0 to 0.5:

∫00.53x2dx=[x3]00.5=(0.5)3=0.125\int_0^{0.5} 3x^2 dx =
[x^3]_0^{0.5} = (0.5)^3
= 0.125∫00.53x2dx=[x3]00.5=(0.5)3=0.125

, Question 6
A fair die is rolled twice. What is the probability that the sum is 7?

A. 1/6
B. 1/8
C. 1/12
D. 1/36

CORRECT DETAILED 100%ANSWER: A
Explanation: Outcomes summing to 7: (1,6), (2,5), (3,4), (4,3),
(5,2), (6,1). Total = 6/36 = 1/6


Question 7
The probability that a student passes a statistics exam is 0.8. If 5
students take the exam, what is the probability that all pass?

A. 0.32768
B. 0.4096
C. 0.512
D. 0.64

CORRECT DETAILED 100%ANSWER: A
Explanation: Multiply probabilities for all independent events:

0.85=0.327680.8^5 = 0.327680.85=0.32768

Question 8
A survey reports the following exam scores: 70, 75, 80, 85, 90.
What is the standard deviation?

A. 7.07
B. 8.00
C. 10.00