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5943600000FOUNDATIONS 12 EXAM REVIEW: STATISTICSThe following table shows the annual salaries of 20 employees of a company. Determine the mean, median, mode and range of the salaries for this company:TitleNumber of EmployeesAnnual SalaryPresident1$250,000Vice-President3$175,000Treasurer1$73,000Accountant2$65,000Salesman9$51,000Secretary4$32,000Mean = Median = Mode = Range =Label the normal distribution curve for Foundations 120 with a mean grade of 85 and a standard deviation of 4.If there are 280 students in the course, how many have a grade less than 77?How many have a grade between 81 and 97?Sketch a bell curve with a large standard deviation…now sketch a bell curve with a small standard deviation. What do the shapes tell you? IQ tests are sometimes used to measure a person’s intellectual capacity at a particular time. IQ scores are normally distributed, with a mean of 100 and a standard deviation of 15. If a person scores 119 on an IQ test, how does this score compare to the scores of the general population?Zac is 195 cm tall. In a recent survey of students at his school, it was determined that the heights of the students are normally distributed, with a mean of 170 cm and a standard deviation of 12.5 cm. What percent of the student’s at Zac’s school are shorter than Zac?What percent of the students are taller than Zac? A manufacturer of smart phones has created a new model. The mean life of this model is 48 months, with a standard deviation of 12 months. The manufacturer has offered a 24-month warranty on this model.Determine the percent of phones that are expected to malfunction during the warranty period.What percent of phones is expected to malfunction during the second and third year of use?Lifespan of Dogs (years)12.913.214.113.912.813.113.213.613.013.412.913.311.812.814.610.414.811.513.513.69.614.513.513.814.413.113.612.812.913.3In a study of the longevity of a particular breed of dog, veterinarians recorded the lifespans of 30 dogs. Does the data approximate a normal distribution?Determine the range and standard deviation of the data. What do these measures tell you about the data?The average daily temperature in Winnipeg, Manitoba, during the month of January is , with a standard deviation of . The average daily temperature in Whitehouse, Yukon, during the month of January is , with a standard deviation of . Compare the temperatures at these two locations in January.How do each of the following impact the size of a confidence interval?Increasing the margin of errorIncreasing the sample sizeIncreasing the confidence levelTwin brothers Eric and Basil are arguing about who did better overall in recent math tests. Eric scored 83 in Algebra and 92 in Geometry, while Basil scored 87 in Algebra and 90 in Geometry. Suppose the scores in Algebra were approximately normally distributed with a mean of 67 and a standard deviation of 15, and the scores in Geometry were approximately normally distributed with a mean of 69 and a standard deviation of 18. Determine the Z-Scores for each brother, in each subject. Who did better overall? A university professor determines that 80% of this year’s Mathematics candidates should pass the final examination. The examination results are expected to be normally distributed with a mean of 62 and a standard deviation of 13. Find the lowest score necessary to pass the examination.A manufacturer of washing machines has determined that the mean life of the machines is 60 months with a standard deviation of 15 months. What length of warranty should be offered if the manufacturer wants to restrict repairs to less than 15 % of all washing machines sold?________________________________________________________________________________________In addition: Review your chapter assignment and unit test.TitleNumber of EmployeesAnnual SalaryTotalsPresident1$250,000250 000Vice-President3$175,000525 000Treasurer1$73,00073 000Accountant2$65,000130 000Salesman9$51,000459 000Secretary4$32,000128 000Solutions:Mean: $78 250.00Median: $51 000 (middle value)Mode: $51 000 (most common)Range: $250 000 - $32 000 = $218 00020 employeesTotal in salary $1 565 000 Grade less than 771962150762000619125571500The standard deviation tells us how tightly your data is clustered around the mean. When the bell curve is flattened, your data is spread out, so you have a large standard deviation- your data is further from the mean. When the bell curve is very steep, your data has a small standard deviation, your data is tightly clustered around the mean.3771900000The value in the Z-score table is 0.8980. This means that an IQ score of 119 is greater than 89.80% of IQ scores in the general population. Now use the Z tables to find the percent of the population to the left of the Z score.97.72 % of the population would be shorter than Zac.b. 100% - 97.22% = 2.28% are taller than Zac.From the tables 0.0228 So 2.28% of the phones malfunction during the warranty period.From the tables 0.1587. So 15.87% of the phones malfunction after 3 years.From the tables .0013. so 0.13% of the phones malfunction after 1 year.15.87% - 0.13% =15.74% of the phones break down during the second and third year of use.Mean: 13.13Median: 13.25Mode: 12.9The data is approximately normal since the mean, median and mode are approximately equal.Range: 5.2Standard Deviation: 1.1The mean temperature in Winnipeg and Whitehorse is the same but the temperature varies more in Whitehorse.Increasing the margin of error increases the size of the confidence interval with a constant sample size.Increasing the sample size decreases the size of the confidence interval.Increasing the confidence level increases the size of the confidence interval with a constant margin of error.Eric did better than 85.77% of the other students in Algebra and better than 89.97% in Geometry.Basil did better than 90.82% of the other students in Algebra and better than 87.9% in Geometry.Basil did better than Eric in Algebra while Basil did better in Geometry. Overall Basil did better.80% are to pass so 20% are unsuccessful.Find the Z value corresponding to 0.2000 Z =-0.84 From the Z tables 15% (.1492) closest Z value is -1.04 ................
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