Quantitative Business Analysis Final Exam-
Section 1: True or false
Q1. In the t distribution or student t distribution, standard deviation controls the shape of the curve. In addition, if the degree of freedom is greater than or equal to 100, the shape of the t distribution is almost the same as normal distribution.
True
False
Q2. For the following conditions: n=20, significant level equal to 10%, the critical Z value is larger than critical t value.
True
False
Q3. Normal distribution is symmetric around the median. The area of one standard deviation from the median under the curve is 68% of the total area under the curve.
True
False
Q4. Type I Error occurs when the others' claim is rejected when it is true. The probability of making a Type I error is known as α, the level of significance.
True
False
Q5. Assume event A is grade≥80, event B is interesting class, if you are given the following contingency table. Even A and Event B are independent or dependent? The values in the table are number of students.
Independent
Dependent
|
Grade
|
interested
|
not interested
|
Total
|
|
lower than 80
|
10
|
20
|
30
|
|
greater or equal to 80
|
40
|
10
|
50
|
|
Total
|
50
|
30
|
80
|
Q6. Tom randomly selected a card from a standard deck (52 cards), the probability to see red Ace is 1/13. This probability is an empirical probability and a marginal probability.
True
False
Q7. In an experiment of tossing a coin ten times, the probability to see heads follows Poisson distribution.
True
False
Q8. Tom and Allen study together andare arguing how to solve the following question:
If sample standard deviation is 20, what sample size is needed to be 95% confident of estimating the population mean with a margin of error of 10?
Tom says this question can not be solved. While Allen said that the sample size is ((-1.96)2202/102).
What is your opinion about this question, you support Tom or Allen.
Q9. The margin of error is 50% of the length of the confidence interval.
True
False
Q10. The sequence of events is important for the conditional probability. The probability to see Event B occurring given that Event A has occurred is P(A|B).
True
False
Section 2: Multiple choices
Q1. In a true or false section which has 5 questions, suppose the probability to get the wrong answer for these 5 questions is the same and equal to 0.3, what is the standard deviation to get right answers (hint, this questions follows binomial distribution)?
A) 0.8
B) 1.05
C) 1.024
D) Not found here
Q2. On average, 2 customers per minute arrive at the bank drive-through window. Assume these arrivals follow the Poisson distribution. What expression is the probability that exactly 3 customers will arrive during the next 15 minutes?
A) p(x=3)=
B) p(x=3)=
C) p(x=3)=
D) p(x=3)=
Q3. In the following distribution, which one is not continuous distribution?
A) Normal distribution
B) Exponential distribution
C) Poisson Distribution
D) Uniform Distribution
4. In the following statement, which statement is correct?
A) The probability to make type I error equals to β
B) The significant level reflects the confidence of researcher's claim.
C) Significance level is denoted as β
D) If α value is decreases, β value is also decreased
5. Which one is Hypothesis test?
A) H0: μ<120; H1: μ≥120;
B) H0: μ≠120; H1: μ<120;
C) H0: μ≥120; H1: μ<120;
D) H0: μ>120; H1: μ≥120;
Section 3: Calculation problems
Q1. My statistic class has 8 students 6 of them are female. In the experiment, I randomly select 4 students (without being replacement) to make a group presentation to the class. What is the probability of the following cases:
a) What is the probability of one of the selected students is male?
b) What is the probability of all selected students are female?
c) What are the mean and standard deviation for question a.
Q2. According to 2014 survey, the average daily rate for the gas in the US is 3.20 dollars/gallon, assume that this daily rate follows a normal distribution with a standard deviation of 0.3 dollars. If you randomly choose a gas station and check the price/gallon,
a) What is the probability to see the gas rate is less than or equal to $3?
b) What is the probability to see the gas rate is greater than $3.5?
c) What is the probability to see the gas rate is between $2.5 and $4.0?
Q3. A random variable follows the uniform distribution between 200 and 500, calculate the following probabilities for the distribution
a) P(250≤x≤370)
b) P(x≥350)
c) What are mean and variance
d) P(x=400)
Q4. A random sample of 30 NCAA Division I men's basketball game during the 2009-2010 season had an average attendance of 4038 with a population standard deviation of 775. Construct a 81.98% confidence interval to estimate the average attendance of an NCAA men's basketball game during the 2009-2010 season (calculation 8 points, conclusion 2 points, pay attention to the format of the conclusion).
Q5. A sporting company operates retail store in New York and Philadelphia. Customers were asked to rate their shopping experience, the results of which are summarized in the following date"
Shopping experience Percentage
Poor 15%
Average 45%
Good 40%
Consider the following information:
67% of customers who rated their "poor" came from Philadelphia. 36% of customers who rate their "average" came from Philadelphia, and 30% of customers who rate their store "Good" came from Philadelphia.
Determine the probability of customer rated the experience as "good", given the fact that the shopping has occurred in Philadelphia.
Q6. Customers arrive at the local Kmart at the rate of 900 customers per day, Assume that the time between customer's arrivals follows exponential distribution and K mart opens 10 hours per day.
a) What is the probability that the next customer will arrive the shop within the next 2 minutes?
b) What is the probability to see the next customer will arrive in exactly 3 minutes?
c) What is standard deviation of question a?