143. The lifetime of a light bulb has density function, f, where f(x) is proportional to , 0<x<5 ,and 0, otherwise.
Calculate the mode of this distribution.
(A) 0.00
(B) 0.79
(C) 1.26
(D) 4.42
(E) 5.00

144. An insurer’s medical reimbursements have density function f, where f(x) is proportional to , for 0 ＜ x ＜ 1, and 0, otherwise. Calculate the mode of the medical reimbursements. (A) 0.00 (B) 0.50 (C) 0.71 (D) 0.84 (E) 1.00

145. A company has five employees on its health insurance plan. Each year, each employee independently has an 80% probability of no hospital admissions. If an employee requires one or more hospital admissions, the number of admissions is modeled by a geometric distribution with a mean of 1.50. The numbers of hospital admissions of different employees are mutually independent. Each hospital admission costs 20,000. Calculate the probability that the company’s total hospital costs in a year are less than 50,000. (A) 0.41 (B) 0.46 (C) 0.58 (D) 0.69 (E) 0.78

146. On any given day, a certain machine has either no malfunctions or exactly one malfunction. The probability of malfunction on any given day is 0.40. Machine malfunctions on different days are mutually independent. Calculate the probability that the machine has its third malfunction on the fifth day, given that the machine has not had three malfunctions in the first three days. (A) 0.064 (B) 0.138 (C) 0.148 (D) 0.230 (E) 0.246

147. In a certain group of cancer patients, each patient's cancer is classified in exactly one of the following five stages: stage 0, stage 1, stage 2, stage 3, or stage 4.i) 75% of the patients in the group have stage 2 or lower.ii) 80% of the patients in the group have stage 1 or higher.iii) 80% of the patients in the group have stage 0, 1, 3, or 4.One patient from the group is randomly selected.Calculate the probability that the selected patient's cancer is stage 1.(A) 0.20(B) 0.25(C) 0.35(D) 0.48(E) 0.65

148. A car is new at the beginning of a calendar year. The time, in years, before the car experiences its first failure is exponentially distributed with mean 2. Calculate the probability that the car experiences its first failure in the last quarter of some calendar year. (A) 0.081 (B) 0.088 (C) 0.102 (D) 0.205 (E) 0.250

149. In a shipment of 20 packages, 7 packages are damaged. The packages are randomly inspected, one at a time, without replacement, until the fourth damaged package is discovered. Calculate the probability that exactly 12 packages are inspected. (A) 0.079 (B) 0.119 (C) 0.237 (D) 0.243 (E) 0.358

150. A theme park conducts a study of families that visit the park during a year. The fraction of such families of size m is , m = 1, 2, 3, 4, 5, 6, and 7. For a family of size m that visits the park, the number of members of the family that ride the roller coaster follows a discrete uniform distribution on the set {1, … , m}. Calculate the probability that a family visiting the park has exactly six members, given that exactly five members of the family ride the roller coaster. (A) 0.17 (B) 0.21 (C) 0.24 (D) 0.28 (E) 0.31

1. For types of error, which of the following statements are TRUE?(1) Systematic error is a consistent error that can be detected and corrected.(2) Random error can be eliminated by improved technique.(3) A key feature of systematic error is that it is reproducible.(4) Systematic error can be detected by using the same method to measure the same quantity.(5) Analyze a known sample to see if you obtain known result can detect systematic eror. Your answer: (A) (2), (4) and (5)； (B) (1), (2) and (3)； (C) (1), (3) and (5)； (D) (2) and (S)； (E) The statements are all true.

2. The end point for the Fajans titration is indicated by the (A) reduction of a colored indicator at the end point. (B) adsorption of a colored indicator on the precipitate at the end point. (C) deprotonation of a colored acid-base indicator at the end point. (D) fornation of a soluble, colored complex at the end point. (E) protonation of a soluble, colored complex at the end point.

3. Which of the following statements about the activity coefficient is NOT TRUE? (A) The activity coefficient decreases as ionic strength increases. (B) The activity corrections are more significant for ions with higher charge. (C) Activity coefficients approach zero when the ionic strength approaches zero. (D) The smaller the ionic size, the larger the deviation from the concentration becomes. (E) The activity of a neutral molecule is assumed to equal its concentration.

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