Exam 5: The Standard Deviation As a Ruler and the Normal Model

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $60,000,mean salary = $140,000,median = $100,000,range = $240,000,IQR = $120,000,first quartile = $70,000,standard deviation = $80,000. Suppose that business has been good and the company gives every employee a $10,000 raise.Give the new value of each of the summary statistics.

-0.73 < z < 2.27

μ = 60.0,4.01% below 53;σ = ?

A town's snowfall in December averages 10 cm with a standard deviation of 10 cm while in February,the average snowfall is 42 cm with a standard deviation of 16 cm.In which month is it more likely to snow 32 cm? Explain.

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $30,000,mean salary = $70,000,median = $50,000,range = $120,000,IQR = $60,000,first quartile = $35,000,standard deviation = $40,000. Do you think the distribution of salaries is symmetric,skewed to the left,or skewed to the right? Explain why.

An English instructor gave a final exam and found a mean score of 70 points and a standard deviation of 5.1 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.Then find the percent of scores above 85.3 points.

Here are some summary statistics for the recent English exam: lowest score = 31,mean score = 66,median = 80.2,range = 79,IQR = 58,Q1 = 26,standard deviation = 8.3.Suppose the students did not study for the exam and each score went down 15%.Tell the new value for each of the summary statistics.Express your answer in exact decimals.

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by N(43,2).Draw and label the Normal model.What percent of snowfall is between 39 cm and 45 cm?

The average number of days absent per student per year at West Valley School is 16 days with a standard deviation of 5 days.How many standard deviations from the mean is of 6 absent days?

An English instructor gave a final exam and found a mean score of 69 points and a standard deviation of 5.8 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.Then find the interval for the central 68% of the scores.

The scores for a recent English exam can be represented by the Normal model N(71,7.0).What score would you expect to be unusually high for this exam?

Two different running shoe manufacturers market running shoes to first time marathon runners.Swift claims a mean shoe life of 600 km,while Enduramax claims a shoe life of 650 km.If the standard deviation for Swift shoes is 54 km and 124 km for Enduramax,which shoe would you purchase before starting your marathon training (where you figure to run 500 km)? Explain.

Suppose that the average amount of sugar a person eats per year is 5 kg with a standard deviation of 1.7 kg.How many standard deviations from the mean is the consumption of 14 kg of sugar?

-0.55 < z < 0.55

z < 0.97

Here are some summary statistics for the recent English exam: lowest score = 31,mean score = 67,median = 81.2,range = 79,IQR = 60,Q1 = 27,standard deviation = 8.6.Between what two values are the middle 50% of the scores found?

Here are some summary statistics for the recent English exam: lowest score = 36,mean score = 71,median = 85.2,range = 74,IQR = 61,Q1 = 28,standard deviation = 8.3.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 140 grams to 207 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 154,252,and 202 grams.A customer makes a special order of a 16 ounce cone.Which of the summary statistics might not change if that data value was added to the distribution?

The test scores from a recent Mathematics test are as follows: 95.5,65.9,93.2,88.6,56.8,50,86.4,54.5,40.9,77.3,79.5,65.9,70.5,77.3,81.8,50,79.5,and 68.2.The mean score was 71.2 with a standard deviation of 15.5.If the Normal model is appropriate,what percent of the scores will be less than 40.2?

Here are some statistics for the annual Wildcat golf tournament: lowest score = 58,mean score = 95,median = 103,range = 92,IQR = 110,Q1 = 38,standard deviation = 15.Suppose it was very windy and all the golfers' scores went up by 7 strokes.Tell the new value for each of the summary statistics.