stats exam 2a

Exam 2 – Stats 1 – Alley – S23 Name________________________________ Ch’s 4-7 Part I - Choose the BEST answer and write it on your answer sheet.  Unclear choices and multiple responses will be marked wrong.  Part II – Answer in the space provided. Formula list and z table are at the back. Answer sheet 1. _________ 2. _________ 3. _________ 4. _________ 5. _________ 6. _________ 7. _________ 8. _________ 9. _________ 10. _________ 11. _________ 12. _________ 13. _________ 14. _________ 15. _________ 16. _________ 17. _________ 18. _________ 19. _________ 20. _________ 1

Part I: Multiple Choice: 20 questions - 3 points each.  1. When using Bayes’ Theorem, initial estimates of the probabilities of events are known as _____ probabilities.   a. subjective   b. posterior   c. conditional   d. prior 2. If A and B are independent events with P ( A ) = 0.5 and P ( B ) = 0.5, then P ( A ∩ B ) is   a. 0.00.   b. 1.00.   c. 0.5.   d. 0.25. 3. If A and B are mutually exclusive events with P ( A ) = 0.3 and P ( B ) = 0.5, then P ( A ∩ B ) =   a. 0.30.   b. 0.15.   c. 0.00.   d. 0.20. 4. If P ( A ) = 0.58, P ( B ) = 0.44, and P ( A ∩ B ) = 0.25, then P ( A ∪ B ) =   a. 1.02.   b. 0.77.   c. 0.11.   d. 0.39. 5. If P ( A ) = 0.50, P ( B ) = 0.40 and P ( A ∪ B ) = 0.88, then P ( B |  A ) =   a. 0.02.   b. 0.03.   c. 0.04.   d. 0.05. 6. A description of the distribution of the values of a random variable and their associated probabilities is called a   a. probability distribution.   b. empirical discrete distribution.   c. bivariate distribution.   d. table of binomial probability. 7. The number of customers that enter a store during one day is an example of   a. a continuous random variable.   b. a discrete random variable. 2

  c. a standard normal distribution.   d. exponential probability distribution. 14. The highest point of a normal curve occurs at   a. one standard deviation to the right of the mean.   b. two standard deviations to the right of the mean.   c. approximately three standard deviations to the right of the mean.   d. the mean. 15. z is a standard normal random variable. The P(-1.96 z 1.4) equals   a. 0.9442.   b. 0.0558.   c. 0.8942.   d. 0.1058. 16. The assembly time for a product is uniformly distributed between 2 to 10 minutes. The probability of assembling the product in less than 6 minutes is   a. 0.   b. 0.50.   c. 0.25.   d. 1. 17. A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 50 and 5, respectively. The standard error of the mean is   a. 0.5.   b. 2.   c. 5.   d. 10. 18. As the sample size increases, the   a. standard deviation of the population decreases.   b. population mean increases.   c. standard error of the mean decreases.   d. standard error of the mean increases. 19. The sample mean x is the point estimator of   a.  μ.   b.  σ.   c.  σ 2   d.  . 4

20. The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the   a. central limit theorem.   b. fact that we have tables of areas for the normal distribution.   c. assumption that the population has a normal distribution.   d. none of these alternatives is correct. Part II: Problem Solving/Short Answer: Answer each question in the space provided. Please write legibly. Fully label any graphs or diagrams. 10 Points each. 1. Tammy is a general contractor and has submitted two bids for two projects ( A and B ). The probability of getting project A is 0.65. The probability of getting project B is 0.77. The probability of getting at least one of the projects is 0.90. a. What is the probability that she will get both projects? b. Are the events of getting the two projects mutually exclusive? Explain, using probabilities. c. Are the two events independent? Explain, using probabilities. 2. At Tennessee Tech, 25% of students live in dormitories. A random sample of 5 students is selected. Use the binomial probability distribution to answer the following questions. a. What is the probability that the sample contains exactly four students who live in the dormitories? b. What is the probability that the sample contains more than three students who live in the dormitories? 5

Chapter 5 Formulas 1. E ( x ) = µ = ∑ xf ( x ) 2. Var ( x ) = σ 2 = ∑ ( x − µ ) 2 f ( x ) 3. f ( x ) = n! x! ( n − x ) ! ∗ p x ∗( 1 − p ) ( n − x ) 4. E ( x ) = µ = np 5. Var ( x ) = σ 2 = np ( 1 − p ) 6. f ( x ) = µ x e − µ x! 7. f ( x ) = C n − x N − R C x R C n N C6 formulas 1. f ( x ) = { 1 b − a ∧ for a≤x ≤b 0 ∧ elsewhere 2. E ( x ) = a + b 2 3. Var ( x ) = ( b − a ) 2 12 4. f ( x ) = 1 σ √ 2 π e −( x − μ ) 2 2 σ 2 5. z = x − μ σ 6. P ( x ≤x 0 )= 1 − e − x 0 μ C7 Formulas 1. E ( x ) = μ 2. σ x = σ √ n 7

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