4. Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is
(A) one
(B) any positive value
(C) zero
(D) any value between 0 to 1

5. If the mean of a normal distribution is negative, (A) the standard deviation must also be negative (B) the variance must also be negative (C) a mistake has been made in the computations, because the mean of a normal distribution cannot be negative (D) None of these alternatives is correct.

6. The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The random variable x satisfies which of the following probability distributions? (A) normal (B) Poisson (C) binomial (D) Not enough information is given to answer this question.

7. As the sample size becomes larger, the sampling distribution of the sample mean approaches a (A) binomial distribution (B) Poisson distribution (C) normal distribution (D) chi-square distribution

8. The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are: (A) \( H_{0}:\mu \geq 35 \) vs. \( H_{a}:\mu < 35 \) (B) \( H_{0}:\mu \leq 35 \) vs. \( H_{a}:\mu >35 \) (C) \( H_{0}:\overline{\mathbf{X}}\geq 35 \) vs. \( H_{a}:\overline{\mathbf{X}} < 35 \) (D) \( H_{0}:\overline{\mathbf{X}}\leq 35 \) vs. \( H_{a}:\overline{\mathbf{X}} >35 \)

9. When the following hypotheses are being tested at a level of significance of a $H_0: \mu \ge 500$$H_a: \mu < 500$ the null hypothesis will be rejected, if the p-value is (A) \( \leq a \) (B) \( >a \) (C) \( = a / 2 \) (D) \( \leq 1 - a / 2 \)

10. An estimator that has small variance (but may be biased) is called precise. An estimator that has small MSE (Mean squared error) is called accurate. To illustrate: A standard 100-gm mass was weighted many, many times, on scale A. Similarly, on scale B, and finally on scale C. The distribution of measurements is summarized belowScale A: $\mu=100.08, \sigma=0.01$ Scale B: $\mu= 99.98, \sigma=0.02$ Scale C: $\mu=100.00, \sigma=0.05$ Which scale is most precise? Which scale is most accurate? (A) B is most precise, A is most accurate (B) A is most precise, B is most accurate (C) A is most precise and is also most accurate (D) B is most precise and is also most accurate (E) Since the population mean is not given, there is no answer to this question. I

1. 一輛摩托車與迎面而來的高速大卡車正面相撞，摩托車全毀。若只考慮量值不考慮方向，則下列有關碰撞瞬間力與加速度的敘述，何者正確？ (A) 摩托車所受力量較大 (B) 卡車所受力量較大 (C) 二車所受力量大小相同 (D) 二車產生的加速度大小相同。

2. 根據克卜勒的行星運動定律，可推知地球繞太陽的運動為？ (A) 變速率橢圓運動 (B) 等速率橢圓運動 (C) 等速率圓周運動 (D) 等加速度圓周運動。

3. 如右圖，一球在一高處以相同速率 v，沿不同方向 A、B、C 拋出，何者瞬間動能最大？ (A) A (B) B (C) C (D) 一樣大。

4. 一週期波在細弦上傳播時，已知某時刻波形如下圖(一)所示；細弦 上某定點的振動距離(y)與時間(t)的關係，如下圖(二)所示，則下列關 於此週期波的敘述何者錯誤？ (A) 波長為 4 公分 (B) 振幅為 0.4 公分 (C) 頻率為 0.125 赫茲 (D) 此波在細弦上的傳播速率為 0.5 公分/秒。

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