111年 - 111 國立臺北大學_碩士班一般入學考試試題_國際企業研究所：統計學#147102

a. The expected frequency of commercial loans in the North region equals 64.49. Give the calculation of this frequency using the data in the contingency table (Table 1) and explain the meaning of this frequency.

b. The CEO of the bank is interested in determining whether the type of loan is related to the region of the country. State the appropriate null and alternative hypotheses.

c. Based on the sample data, what should be concluded about the hypotheses? Perform the test using a significance level of 0.05. Please write all relevant findings of your test procedure in your answer sheet.

d. Explain your conclusion in plain English.

e. The CEO of the bank is also interested in determining whether the amount of loan is related to the region of the country. Is it appropriate to use Chi-square test to determine? Why?

a. Give the type of distribution with the parameters of the variable \( p \).

b. What is the probability that \( p \) is less than 0.35?

a. Construct a tree diagram in which all options concerning the gender of the chosen students together with the probabilities are given if the teacher randomly picks two students.

b. Calculate the probability that one of the students is female and the other is male. Show your calculations.

c. Calculate the probability that both students are female.

(1) 旅客行李之樣本平均重量 \( X \) 之抽樣分配為？__________

(2) 以 \( \mu = 28 \) 公斤為中心，而機率為0.95之X的區間為？__________

(3) 樣本平均重量 \( X \) 落在 [26.8, 29.2] 之間的機率為？__________

(1)今客戶要求的規格為 \( 199\pm 4 \) 公克，過重或過輕均為不合格，試問在目前的機器設備下，不合格的比例為__________；

(2)若該蘋果產品的標準差仍維持4公克，欲使其重量超過210公克的機率等於 \( 5\% \) ，則平均重量應訂為__________。

(1) 隨機變數 \( X \) 的平均數 \( = \) __________，與變異數 \( = \) __________

(2) 若你改變心意，想加碼投資到 \( 10萬元，則你可能的淨回收(net payoff)的平均數 \) \( = \)  __________，與變異數 \( = \) __________

(1) 隨機變數 \( X \) 的平均數 \( = \)  __________及變異數 \( = \) __________；

(2) \( \mathrm{P}(\mathrm{X} = 0) = \)  __________，和 \( \mathrm{P}(\mathrm{X}\geq 2) = \) __________

(1) 此組樣本的變異數大於 18.69 公克的機率 =_____________；

(2) \( P(5.5728 \leq S^2 \leq 22.063) = ? \)__________；