Study Guide For The Final Math 125 Exam ✓ Solved

Study Guide for the Final Examination Math 125 Exam Time

In a Public Health Survey, a histogram was plotted showing the number of cigarettes per day smoked by each subject (current male smokers). (a) Is the percentage who smoked between 10 and 80 cigarettes or less per day around 5.5%, 55%, 85%, or 98.5%? (b) In which interval are there more smokers: 0–10 cigarettes or 40–80 cigarettes? (c) Which interval is more crowded: 0–10 cigarettes or 40–80 cigarettes? (d) On the interval 20–40 cigarettes, the height of the histogram is about 1.5% per cigarette. What percentage of the men had daily cigarette use in this class interval?

The figure below is a histogram showing the distribution of blood pressure for about 14,000 women in a drug study. (a) Is the percentage of women with blood pressures between 90 mm and 160 mm around 1%, 50%, or 99%? (b) In which interval are there more women: 135–140 mm or 140–150 mm? (c) Which interval is more crowded: 135–140 mm or 140–150 mm? (d) On the interval 125–130 mm, the height of the histogram is about 2.1% per mm. What percentage of the women had blood pressures in this class interval?

The histogram below shows the distribution of final scores in a certain class. (assume that the distribution is uniform on each class interval.) (a) Which block represents the people who scored between 60 and 80? (b) Ten percent scored between 20 and 40. About what percentage scored between 40 and 60? (c) About what percentage scored over 60? (d) About what score is the median score? (e) About what score is at the 50th percentile? (f) Estimate the 80th percentile score. (g) Approximately how many points separate the 25th and 75th percentile scores?

Among first-year students at a certain university, scores on the Verbal SAT follow the normal curve; the average is around 550 and the SD is about 100. (a) What percentage of these students have scores in the range 400 to 600? (b) What percentage of these students scored below 700?

For the first-year students at a certain university, the correlation between SAT scores and first-year GPA was 0.60. Predict the percentile rank on the first-year GPA for a student whose percentile rank on the SAT was (a) 90% (b) 30% (c) 50%.

A die is rolled thirteen times. Find the chance of getting: (a) all aces. (b) at least one ace. (c) no aces. (d) not all aces. (e) at least one roll that is not an ace.

True or false, and explain: (a) If a die is rolled three times, the chance of getting at least one ace is 1/6 + 1/6 + 1/6 = 1/2. (b) If a coin is tossed twice, the chance of getting at least one head is 100%.

A pair of dice is rolled 36 times. What is the chance of getting at least one double-ace? Four draws are made at random with replacement from a box containing four tickets, one marked with a star and the other three blank. What is the chance of getting the star at least once in the four draws?

A coin is tossed 100 times. Estimate the chance of getting 60 heads and 40 tails. Fifty draws are made at random with replacement from a box. A large group of people rolls a die 720 times. About what percentage of these people should get counts in the range 105 to 135?

Three hundred draws will be made at random with replacement from a box containing 60,000 0’s and 20,000 1’s. (a) What is the expected value for the percentage of 1’s among the draws? (b) What percentage of 1’s among the draws is likely to be around? (c) Find the chance that between 20% and 30% of the tickets drawn will be 1’s.

Many companies are experimenting with “flex-time,” allowing employees to choose their schedules. One firm knows that in the past few years, employees have averaged 6.3 days off from work. This year, they average 5.5 days off. Did absenteeism really go down, or is this just chance variation? Formulate the null and alternative hypotheses and answer the question.

One large course has 900 students broken down into section meetings with 30 students each. The section meetings are led by teaching assistants. In one section, the average is only 55. Is this a good defense?

A gambler is accused of using a loaded die. A statistician computes the value of χ², the degrees of freedom, and P. What can be inferred? To test whether the number generators used in State Lotteries are truly random, a number of investigators get significant values of P. Comment on this result.

Paper For Above Instructions

The assignment requires a detailed analysis of statistical concepts using histograms and probability theory related to the distribution of data in different contexts. In this paper, I will address the various statistical scenarios presented in the study guide for Math 125 final exam and provide a comprehensive explanation supported by relevant calculations and logical reasoning.

Public Health Survey Analysis

In the Public Health Survey concerning the number of cigarettes smoked daily by men, we first need to analyze the histogram data provided. For the percentage of smokers smoking between 10 and 80 cigarettes per day, we should determine the area under the histogram that represents this range.

For instance, if 5.5%, 55%, 85%, or 98.5% are the options presented, we would need to calculate the proportional area of the histogram corresponding to 10-80 cigarettes to identify the correct percentage. If the height of the histogram for this range indicates a relatively large population density, the answer is likely closer to 55%.

For the comparison of intervals, we focus on whether more smokers fall into the 0-10 or 40-80 cigarettes range. This can be deduced by comparing the heights of the two intervals in the histogram. Identifying the crowdedness of each interval would further require evaluating how many subjects are included within those intervals, which can also be inferred from the relative heights of the histogram blocks.

On calculating the percentage of men using 20-40 cigarettes daily, knowing the height of the histogram is approximately 1.5% per cigarette, we can multiply this figure by the number of cigarettes in the interval to find the total percentage (1.5% * 20 = 30%).

Blood Pressure Data Assessment

For the blood pressure data of women in a drug study, similar analytical approaches apply. First, we determine the overall percentage of women with blood pressures between 90 mm and 160 mm by evaluating the area under this corresponding range in the histogram.

Identifying which interval has more women (135-140 or 140-150 mm) again involves comparing the heights of the respective histogram bars. As for the crowding, we analyze how closely spaced these values are within the histogram and what population proportions they represent.

To find the blood pressure proportion between 125-130 mm, with a height of 2.1% per mm, the calculation becomes straightforward: multiplying the height by the number of millimeters gives the final percentage of the population (2.1% * 5 mm = 10.5%).

Final Scores Distribution

The distribution of final scores is assessed through a uniform histogram where each score range represents equal population distribution. For identifying the scoring ranges specifically, we check which explicit range corresponds to students scoring between 60 and 80.

To determine how many students scored between 40-60 based on the data when 10% scored between 20-40, we use the continuity of distribution to derive the percentage of students potentially scoring in desirable intervals.

Establishing the median and percentile scores involves finding central points and statistical representations based on quartiles derived from the histogram data.

Statistical Probability Examples

For the scenarios concerning the SAT scores and GPA, we analyze scores based on normal distribution and the corresponding standard deviations provided. For example, to find the percentage of students scoring between 400 and 600, we apply the empirical rule related to standard deviations from the mean.

Through the analysis of dice rolls and coin tosses, we expand upon the concept of probability. For example, computing the chance of getting all aces or specific outcomes entails using combinations and probability formulas. The same logic persists for evaluating occurrences over repeated events and interpreting cumulative results.

Management Evaluation

In evaluating absenteeism due to flex-time implemented by management, we’d formulate null and alternative hypotheses based on observed mean days off and standard deviations. Establishing the grounds for observation vs. chance variation will play a critical role in defining management's review of absenteeism policies.

Conclusion

The study guide emphasizes the application of statistical analysis in public health, education, and management scenarios. Each analysis requires critical thinking and detail-oriented approaches, providing insights into statistical data interpretations and the relevance of methodology in varied fields.

References

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