Đề Thi FE MAS291 - SP26 - B5 - FE - RE

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MAS291 SP26 B5 FE RE

Câu 1​

Type: Multiple Choice Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called

• A. statistical inference.
  
  
  
  
• 
  
  B. descriptive statistics.
  
  
  
  
• C. sampling.
  
  
  
  
• D. the scientific method.
  
  

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Câu 2​

Type: Choose 1 answer | Multiple Choice A method of gathering data while the subjects of interest are in their natural environment, often unaware they are being watched, is known as

• 
  
  A. observation.
  
  
  
  
• B. experiments.
  
  
  
  
• C. retrospective
  
  
  
  
• D. None of the other choices is correct
  
  

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Câu 3​

In probability, what is a sample space defined as?

• A. a repeatable process, or activity, with a number of possible outcomes
  
  
  
  
• B. a collection of one or more possible outcomes from an activity, which can be described as having certain characteristics
  
  
  
  
• 
  
  C. the set of all possible outcomes of an activity or experiment
  
  

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​

Type: Choose 1 answer | Multiple Choice A manufacturer produces mobile phones, some of which may be defective. Suppose you sequentially select two mobile phones at random from the production line and test them to determine whether they operate well (G) or are defective (B) (without replacement). Let A denote the event "at least one mobile phone operates well." Which of the following sets lists all outcomes belonging to A.

• A. (GB)
  
  
  
  
• B. (GG)
  
  
  
  
• C. (BB)
  
  
  
  
• D. (BG, GB, GG)
  
  

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Câu 5​

Type: Choose 1 answer | Multiple Choice Each of the possible four outcomes of a random experiment is equally likely. The sample space is {a, b, c, d}. Let A denote the event {a, b}, and let B denote the event {a, c}. Determine $P(A\cup B)$.

• A. 0.75
  
  
  
  
• B. 1.0
  
  
  
  
• C. 0.6
  
  
  
  
• D. 0.016
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 6​

Type: Choose 1 answer | Multiple Choice In a telephone survey of 1000 adults, respondents were classified according to whether they currently had a child in college (D/E) and their opinion on loan burden (A/B/C). The proportions are:

• Child in College (D): A=0.35, B=0.08, C=0.01
  
  
  
  
• No Child in College (E): A=0.25, B=0.2, C=0.11 What is the probability that the respondent has a child in college (D) or thinks that the loan burden is too high (A)?
  
  
  
  
• A. 0.56
  
  
  
  
• B. 0.44
  
  
  
  
• C. 0.69
  
  
  
  
• D. 0.6
  
  

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Câu 7​

Type: Multiple Choice A lot of 150 semiconductor chips contains 30 that are defective. Two are selected randomly, without replacement, from the lot. What is the probability that the second one selected is defective given that the first one was defective?

• A. 0.2
  
  
  
  
• B. 0.039
  
  
  
  
• C. 0.8
  
  
  
  
• D. 0.195
  
  

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Câu 8​

Type: Choose 1 answer | Multiple Choice If men constitute 47% of the population and tell the truth 78% of the time, while women tell the truth 63% of the time, what is the probability that a person selected at random will answer a question truthfully?

• A. 0.78
  
  
  
  
• B. 0.52
  
  
  
  
• C. 0.49
  
  
  
  
• D. 0.70
  
  

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Câu 9​

Type: Multiple Choice Suppose $P(A)=0.4$ and $P(A\cup B)=0.7.$ If A and B are independent events, then the value of $P(B)$ is:

• A. 0.5
  
  
  
  
• B. 0.3
  
  
  
  
• C. 0.55
  
  
  
  
• D. 0.6
  
  

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Câu 10​

Type: Choose 1 answer | Multiple Choice Bag A contains 15 white and 10 black balls while another Bag B contains 10 white and 15 black balls. One ball is drawn at random from one of the bags and it is found to be white. Find the probability that it was drawn from Bag B.

• A. 0.4
  
  
  
  
• B. 0.5
  
  
  
  
• C. 0.6
  
  
  
  
• D. 0.7
  
  

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Câu 11​

Type: Multiple Choice Which of the following is NOT TRUE about continuous random variables?

• A. ...takes an infinite number of possible values.
  
  
  
  
• B. ...is usually about measurement.
  
  
  
  
• C. ...is quantitative data.
  
  
  
  
• D. ...has a countable infinite range.
  
  

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Câu 12​

Type: Choose 1 answer | Multiple Choice A batch of 300 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected. What is the range of the random variable?

• A. Integers from 0 to 10
  
  
  
  
• B. Integers from 1 to 10
  
  
  
  
• C. Integers from 0 to 300
  
  
  
  
• D. Integers from 1 to 291 (Note: $300 - 10 + 1 = 291$)
  
  

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Câu 13​

Type: Choose 1 answer | Multiple Choice The discrete random variable X has the probability mass function $f(0)=0.6561, f(1)=0.2916, f(2)=0.0486, f(3)=0.0036, f(4)=0.0001$. Find $P(2\le X<3)$.

• A. 0.7084
  
  
  
  
• B. 0.0522
  
  
  
  
• C. 0.0486
  
  
  
  
• D. 0.6875
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 14​

Type: Choose 1 answer | Multiple Choice The cumulative distribution function $F(x)$ of a discrete random variable X is given. (Graph shows $F(x)$ jumps at $x=1$ to 0.2 and at $x=3$ to 1.0). Use this graph to find $P(0.5 < X < 3)$.

• A. 0.2
  
  
  
  
• B. 0.4
  
  
  
  
• C. 0.6
  
  
  
  
• D. 0.8
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 15​

Type: Multiple Choice The range of the random variable X is $\{0, 1, 2, 3, x\}$ where x is unknown. If each value is equally likely and the mean of X is 6, determine x.

• A. 4
  
  
  
  
• B. 10
  
  
  
  
• C. 24
  
  
  
  
• D. 18
  
  
  
  
• E. 20
  
  
  
  
• F. None of the other choices is correct
  
  

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Câu 16​

Type: Choose 1 answer | Multiple Choice The random variable X has the discrete uniform distribution $P(X=x)=1/3$ for $x=1, 4, 10$. Find $E(X)$.

• A. 5.0
  
  
  
  
• B. 5.5
  
  
  
  
• C. 6.0
  
  
  
  
• D. 4.0
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 17​

Type: Multiple Choice A basketball player has made 70% of his foul shots. If he shoots 3 foul shots, what is the probability that he makes all of them?

• A. 0.09
  
  
  
  
• B. 0.213
  
  
  
  
• C. 0.098
  
  
  
  
• D. 0.343 ($0.7^3 = 0.343$)
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 18​

Type: Choose 1 answer | Multiple Choice Given the probability of hitting a target is 0.7. What is the probability that the sniper needs at least four shots to hit the target for the first time?

• A. 0.9919
  
  
  
  
• B. 0.0189
  
  
  
  
• C. 0.973
  
  
  
  
• D. 0.027 ($(1-0.7)^3 = 0.027$)
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 19​

Type: Multiple Choice Given X is a hyper-geometric random variable with $N=10, K=5, n=6$. Compute the mean of X.

• A. 3
  
  
  
  
• B. 4
  
  
  
  
• C. 1
  
  
  
  
• D. 2
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 20​

Type: Choose 1 answer | Multiple Choice The number of lightning strikes follows a Poisson distribution with mean 3.9. Find the probability that in a randomly selected year, the number of strikes is 2.

• A. 0.2001
  
  
  
  
• B. 0.0128
  
  
  
  
• C. 0.1539
  
  
  
  
• D. 0.2617
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 21​

Type: Choose 1 answer | Multiple Choice Time to failure for a laser is modeled by an exponential distribution with $\lambda=0.00004$. Find the probability that the laser will last at least 20000 hours.

• A. 0.45 ($e^{-0.00004 \times 20000} \approx 0.449$)
  
  
  
  
• B. 0.65
  
  
  
  
• C. 0.74
  
  
  
  
• D. 0.55
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 22​

Type: Choose 1 answer | Multiple Choice Let $f(x)=0.5$ for $0<x<2$ be the PDF of a continuous random variable. Find $P(X<1.5)$.

• A. 0.25
  
  
  
  
• B. 0.75
  
  
  
  
• C. 0.5
  
  
  
  
• D. 0
  
  
  
  
• E. None of the other choice is correct
  
  

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Câu 23​

Type: Choose 1 answer Let X be a continuous random variable with CDF $F(x) = 1-e^{-4x}$ for $x>0$. Determine $P(-1<X<1)$.

• A. 0.9817 ($1-e^{-4} \approx 0.9817$)
  
  
  
  
• B. 0.0183
  
  
  
  
• C. 0.5655
  
  
  
  
• D. 0.4345
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 24​

Type: Choose 1 answer | Multiple Choice Let X be a random variable. Given $E(X)=0,$ find $E(3X+1)$.

• A. 1
  
  
  
  
• B. 3
  
  
  
  
• C. 4
  
  
  
  
• D. 2
  
  
  
  
• E. None of the other choices is true
  
  

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Câu 25​

Type: Multiple Choice Cleanser pump rate is described by a uniform distribution over the interval 9.5 to 13.5 gallons per minute. Find the variance of the distribution.

• A. 8.33
  
  
  
  
• B. 1.33 ($\frac{(13.5-9.5)^2}{12} = \frac{16}{12} = 1.33$)
  
  
  
  
• C. 44.08
  
  
  
  
• D. 0.75
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 26​

Type: Choose 1 answer | Multiple Choice X has a normal distribution with mean = 30 and SD = 5. Find $P(X < 32)$. Let $P(Z<0.4)=0.6554, P(Z<0.2)=0.5793$.

• A. 0.3446
  
  
  
  
• B. 0.4207
  
  
  
  
• C. 0.6554
  
  
  
  
• D. 0.5793
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 27​

Type: Multiple Choice GPAs are normally distributed with mean 2.6 and SD 0.4. What percentage of students have a GPA between 2.2 and 3? (Given $P(Z<1)[cite_start]=0.8413, P(Z<-1)=0.1613$).

• A. 68%
  
  
  
  
• B. 84.13%
  
  
  
  
• C. 99.7%
  
  
  
  
• D. 89%
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 28​

Type: Choose 1 answer | Multiple Choice X has a Poisson distribution with mean 140. Use normal approximation to find $P(X<130)$. (Given $P(Z<-0.89)[cite_start]=0.1867$).

• A. None of the other choices is correct
  
  
  
  
• B. 0.6293
  
  
  
  
• C. 0.5122
  
  
  
  
• D. 0.8413
  
  
  
  
• E. 0.9332
  
  
  
  
• Result (based on values): Probable answer is 0.1867 (not listed as A-E clearly but indicated by given Z-value).

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Câu 29​

Type: Multiple Choice Fuel octane ratings: 88.2, 93.8, 86.5. Find the sample variance.

• A. 14.59
  
  
  
  
• B. 3.82
  
  
  
  
• C. 4.26
  
  
  
  
• D. 18.34
  
  

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Câu 30​

Type: Choose 1 answer | Multiple Choice Sample data: 25, 11, 6, 4, 2, 17, 9, 6. Find the sample mean.

• A. 3
  
  
  
  
• B. 10
  
  
  
  
• C. 8
  
  
  
  
• D. 7
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 31​

Type: Choose 1 answer | Multiple Choice Stem and leaf diagram:

• 0: 5, 5, 6
• 1: 1, 2, 3, 4, 6
• 2: 0, 1, 2What is the third quartile $Q_{3}$?
  
  
  
  
• A. 20
  
  
  
  
• B. 6
  
  
  
  
• C. 14
  
  
  
  
• D. 22
  
  
  
  
• E. 13
  
  
  
  
• F. 15 (Correct based on $n=11$)
  
  

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Câu 32​

Type: Choose 1 answer | Multiple Choice Given a table of 50 data points, what is the relative frequency of the interval $90\le x<100$?

• A. 12% (6 occurrences: 98, 97, 96, 97, 96, 97)
  
  
  
  
• B. 10%
  
  
  
  
• C. 0.50%
  
  
  
  
• D. 60%
  
  
  
  
• E. None of the other choices
  
  

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Câu 33​

Type: Multiple Choice A score at the 2nd quartile means: (i) 50th percentile, (ii) median. Which statements are correct?

• A. (i)
  
  
  
  
• B. (ii)
  
  
  
  
• C. Both (i) and (ii)
  
  
  
  
• D. None of the other choices is correct
  
  

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Câu 34​

Type: Choose 1 answer | Multiple Choice Suppose $\mu=16, \sigma^2=20, n=100$. What is the standard deviation for the sample mean ($\sigma_{\bar{x}}$)?

• A. 0.45 ($\sqrt{20/100} = \sqrt{0.2} \approx 0.447$)
  
  
  
  
• B. 0.2
  
  
  
  
• C. 0.16
  
  
  
  
• D. 0.02
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 35​

Type: Choose 1 answer | Multiple Choice Population 1: $n_1=16, \mu_1=75, \sigma_1=8$. Population 2: $n_2=9, \mu_2=70, \sigma_2=12$. Find $P(\overline{X}_1-\overline{X}_2>5.5)$. Let $P(Z<0.11)=0.5438$.

• A. 0.4562 ($1 - 0.5438 = 0.4562$)
  
  
  
  
• B. 0.5438
  
  
  
  
• C. 0.6438
  
  
  
  
• D. 1
  
  
  
  
• E. None of the others
  
  

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Câu 36​

Type: Multiple Choice Average score $\mu=79, \sigma=5, n=100$. Find the probability that the average of 100 golfers exceeded 80. (Given $P(Z<2)=0.9772$).

• A. 0.3707
  
  
  
  
• B. 0.1293
  
  
  
  
• C. 0.0228 ($1 - 0.9772 = 0.0228$)
  
  
  
  
• D. 0.4772
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 37​

Type: Choose 1 answer | Multiple Choice A 97% confidence interval for CEO compensation is (2181260, 5836180). Which interpretation is correct?

• A. We are 97% confident that the average total compensation of all CEOs in the Service industry falls in the interval.
  
  
  
  
• B. We are 97% confident that the mean of the sampled CEOs falls in the interval.
  
  
  
  
• C. 97% of the population CEOs will fall in this interval.
  
  
  
  
• D. 97% of the sampled values fell between these numbers.
  
  

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Câu 38​

Type: Choose 1 answer | Multiple Choice $n=25, \bar{x}=81.5, s=10.2$. Construct a 95% CI for the population mean. Let $t_{0.025, 24} = 2.06$.

• A. (56.12, 78.34)
  
  
  
  
• B. (77.30, 85.70)
  
  
  
  
• C. (87.12, 98.32)
  
  
  
  
• D. (66.35, 69.89)
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 39​

Type: Choose 1 answer | Multiple Choice $n=81$, 64 have health insurance. Construct a 90% CI for the percentage. Let $z_{0.05}=1.645$.

• A. (67.4%, 90.7%)
  
  
  
  
• B. (73.0%, 85.0%)
  
  
  
  
• C. (70.1%, 87.9%)
  
  
  
  
• D. (71.6%, 86.5%)
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 40​

Type: Choose 1 answer | Multiple Choice Claim: average volume is at least 2000 ml. Express null and alternative hypotheses.

• A. (i) $H_0: \mu = 2000, H_1: \mu > 2000$
  
  
  
  
• B. (ii) $H_0: \mu = 2000, H_1: \mu < 2000$
  
  
  
  
• C. (iii) $H_0: \mu < 2000, H_1: \mu \ge 2000$
  
  
  
  
• D. (iv) $H_0: \mu > 2000, H_1: \mu \le 2000$
  
  

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Câu 41​

Type: Choose 1 answer | Multiple Choice Test $H_0: \mu=110$ vs $H_1: \mu>110$. $n=16, \sigma=10, \bar{x}=113.5$. Significance level 5%, $Z_{0.05}=1.645$.

• A. Reject Ho ($z = (113.5-110)/(10/4) = 1.4$. Wait, $1.4 < 1.645$, so Fail to reject).
  
  
  
  
• B. Fail to reject Ho (Correct: $z=1.4$)
  
  

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Câu 42​

Type: Choose 1 answer | Multiple Choice Claim $\mu=1000$. $n=29, \bar{x}=988, s=30$. Calculate the test statistic.

• A. -2.15 ($t = (988-1000)/(30/\sqrt{29}) \approx -2.15$)
  
  
  
  
• B. 1.96
  
  
  
  
• C. 3.21
  
  
  
  
• D. -1.32
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 43​

Type: Choose 1 answer | Multiple Choice Survey: 70% favor euthanasia. Test if this holds for over-55 group ($n=900, x=684$) at 5% level.

• A. (i) Test statistic $z_{0}=3.93$, reject the null hypothesis
  
  
  
  
• B. (ii) $z_0=3.03$, fail to reject
  
  
  
  
• C. (iii) $z_0=8.93$, reject
  
  
  
  
• D. (iv) $z_0=3.93$, fail to reject
  
  

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Câu 44​

Type: Choose 1 answer | Multiple Choice Test if men's age > women's age. Men: $\bar{x}_1=64.5, n_1=35, \sigma_1=3.0$. Women: $\bar{x}_2=63.6, n_2=39, \sigma_2=3.5$. Find the test statistic.

• A. 1.19 ($z = (64.5-63.6)/\sqrt{3^2/35 + 3.5^2/39} \approx 1.19$)
  
  
  
  
• B. -2.23
  
  
  
  
• C. 2.07
  
  
  
  
• D. -1.78
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 45​

Type: Multiple Choice Compare mpg of two brands. Brand 1: $n=5, \bar{x}=29.5, s=7.4$. Brand 2: $n=8, \bar{x}=31.6, s=8.4$. Variances equal, normal distribution. Which test is most appropriate?

• 
  
  A. two-sample independent t-test
  
  
  
  
• B. two-sample z-test
  
  
  
  
• C. two-sample proportion z-test
  
  
  
  
• D. none of the above
  
  

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Câu 46​

Type: Choose 1 answer | Multiple Choice $n_1=200, x_1=10$. $n_2=200, x_2=8$. Construct a 99% CI on the difference in fractions defective. $z_{0.005}=2.58$.

• A. (-0.043, 0.063)
  
  
  
  
• B. (-0.038, 0.058)
  
  
  
  
• C. (-0.038, 0.063)
  
  
  
  
• D. (-0.043, 0.058)
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 47​

Type: Choose 1 answer | Multiple Choice Regression model $y=a+bx$ for data: $x=\{12, 15, 20, 25\}, y=\{69, 60, 55, 48\}$.

• A. $85.18 - 1.51x$
  
  
  
  
• B. $85.18x - 1.51$
  
  
  
  
• C. $85.18 + 1.51x$
  
  
  
  
• D. $85.18x + 1.51$
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 48​

Type: Choose 1 answer | Multiple Choice Using $\hat{y}=1.6+1.1x$ for data $x=\{0,1,2,4,5\}, y=\{1,3,4,7,6\}$, find $SS_E$.

• A. 2.700
  
  
  
  
• B. 3.018
  
  
  
  
• C. 1.837
  
  
  
  
• D. 4.550
  
  
  
  
• E. None of the other choices is correct
  
  

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Câu 49​

Type: Choose 1 answer | Multiple Choice Linear regression for Math (X) and Finance (Y) grades. $n=5, \hat{\sigma}=1.43, \hat{\beta}_0=3.18$. Calculate test statistic for $H_0: \beta_0=0$.

• A. 1.18
  
  
  
  
• B. 1.38
  
  
  
  
• C. 1.58
  
  
  
  
• D. 1.78
  
  

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Câu 50​

Type: Multiple Choice Correlation coefficient between X and Y is positive and close to 1. The relationship is:

• 
  
  A. a strong linear relationship and as X increases, Y increases
  
  
  
  
• B. a weak linear relationship and as X increases, Y decreases
  
  
  
  
• C. a weak linear relationship and as X increases, Y increases
  
  
  
  
• D. a strong linear relationship and as X increases, Y decreases
  
  
  
  
• E. None of the other choices is correct