DNA molecules consist of chemically linked sequences of the bases adenine, guanine, cytosine, and thymine, denoted A, G, C, and T. A sequence of three bases is called a codon. A base may appear more than once in a codon. a. How many different codons are there? b. The bases A and G are purines, while C and T are pyrimidines. How many codons are there whose first and third bases are purines and whose second base is a pyrimidine? c. How many codons consist of three different bases?

Previous studies have shown that urban bus drivers have an extremely stressful job, and a large proportion of drivers retire prematurely with disabilities due to occupational stress. These stresses come from a combination of physical and social sources such as traffic congestion, incessant time pressure, and unruly passengers. In the paper, “Hassles on the Job: A Study of a Job Intervention With Urban Bus Drivers” (Journal of Organizational Behavior, Vol. 20, pp. 199-208), G. Evans et al. examined the effects of an intervention program to improve the conditions of urban bus drivers. Among other variables, the researchers monitored diastolic blood pressure of bus drivers in downtown Stockholm, Sweden. The data, in millimeters of mercury (mm Hg), on the WeissStats CD are based on the blood pressures obtained prior to intervention for the 41 bus drivers in the study. Use the technology of your choice to do the following. a. Obtain a normal probability plot, boxplot, histogram, and stem-and-leaf diagram of the data. b. Based on your results from part (a), can you reasonably apply the one-mean t-test to the data? Explain your reasoning. c. At the 10% significance level, do the data provide sufficient evidence to conclude that the mean diastolic blood pressure of bus drivers in Stockholm exceeds the normal diastolic blood pressure of 80 mm Hg?

The four organs from which fluid output occurs are the _____, _____, _____, and _____.

An office has three smoke detectors. In case of fire, each detector has probability $0.9$ of detecting it. If a fire occurs, what is the probability that at least one detector detects it?

The probability that a bearing fails during the first month of use is 0.12. What is the probability that it does not fail during the first month?

All the fourth-graders in a certain elementary school took a standardized test. A total of 85% of the students were found to be proficient in reading, 78% were found to be proficient in mathematics, and 65% were found to be proficient in both reading and mathematics. A student is chosen at random. a. What is the probability that the student is proficient in mathematics but not in reading? b. What is the probability that the student is proficient in reading but not in mathematics? c. What is the probability that the student is proficient in neither reading nor mathematics?

Six hundred paving stones were examined for cracks, and 15 were found to be cracked. The same 600 stones were then examined for discoloration, and 27 were found to be discolored. A total of 562 stones were neither cracked nor discolored. One of the 600 stones is selected at random. a. Find the probability that it is cracked, discolored, or both. b. Find the probability that it is both cracked and discolored. c. Find the probability that it is cracked but not discolored.

Let S be the event that a randomly selected college student has taken a statistics course, and let C be the event that the same student has taken a chemistry course. Suppose P(S) = 0.4, P(C) = 0.3, and $P(S \cap C)=0.2.$ a. Find the probability that a student has taken statistics, chemistry, or both. b. Find the probability that a student has taken neither statistics nor chemistry. c. Find the probability that a student has taken statistics but not chemistry.

In horse racing, one can make a trifecta bet by specifying which horse will come in first, which will come in second, and which will come in third, in the correct order. One can make a box trifecta bet by specifying which three horses will come in first, second, and third, without specifying the order. a. In an eight-horse field, how many different ways can one make a trifecta bet? b. In an eight-horse field, how many different ways can one make a box trifecta bet?

A quiz consists of three true–false questions and two multiple-choice questions with five choices each. How many different sets of answers are there?

Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. The joint probability mass function of X and Y is as follows:

$$\begin{matrix} & \text{y}\\ \text{x} & \text{0} & \text{1} & \text{2} & \text{3}\\ \text{0} & \text{0.13} & \text{0.10} & \text{0.07} & \text{0.03}\\ \text{1} & \text{0.12} & \text{0.16} & \text{0.08} & \text{0.04}\\ \text{2} & \text{0.02} & \text{0.06} & \text{0.08} & \text{0.04}\\ \text{3} & \text{0.01} & \text{0.02} & \text{0.02} & \text{0.02}\\ \end{matrix}$$

a. Find the marginal probability mass function $p_{x}(x)$ b. Find the marginal probability mass function $p_{\gamma}(y)$ c. Find $\mu_{x}$ d. Find $\mu_{Y}$ e. Find $\sigma_{X}$ f. Find $\sigma_{Y}$ g. Find Cov(X, Y ). h. Find $\rho_{x, y}$

A metallurgist is designing an experiment to determine the effect of flux, base metal, and energy input on the hardness of a weld. She wants to study four different fluxes, two different base metals, and three different amounts of energy input. If each run of the experiment involves a choice of one flux, one base metal, and one amount of energy input, how many different runs are possible?

A system contains two components, A and B. The system will function only if both components function. The probability that A functions is 0.98, the probability that B functions is 0.95, and the probability that either A or B functions is 0.99. What is the probability that the system functions?

A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3 different heating systems, a garage or carport, and a patio or screened porch. How many different plans are available to this buyer?