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

The lengths of human pregnancies can be described by a Normal model with a mean of 268 days and a standard deviation of 15 days.What percentage can we expect for a pregnancy that will last at least 300 days?

The average size of forest fires last year was 968 acres with a standard deviation of 182 acres.How many standard deviations from the mean is a forest fire consuming 245 acres?

The amount of Jen's monthly phone bill is normally distributed with a mean of $55 and a standard deviation of $8.Draw and label the Normal model for Jen's monthly phone bill.In what interval would you expect the central 68% of bills to be found?

Here are some summary statistics for last years basketball team scoring output: lowest score = 19 points,mean = 55 points,median = 49 points,range = 96 points,IQR = 52,Q1 = 22,standard deviation = 6 points.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

After increased patrol,cars on a road travel at speeds averaging 55 km/h.If 93% of vehicles travel below 68 km/h,what approximate standard deviation could represent this model (assuming a Normal model is appropriate)?

z > -1.82

For a recent English exam,use the Normal model N(73,9.2)to find the score that represents the 30th percentile.

The average attendance for your local hockey team is 450,000 per game.The attendance during the last game was only 320,000 which corresponded to a z-score of -16.25.Find the standard deviation.

The annual snowfall in a town (in cm)can be represented by the Normal model N(41,5.3).What amount of snowfall would you expect to be unusually low for this town?

Mario's poker winnings average $319 per week with a standard deviation of $56.How many standard deviations from the mean is winning $195?

μ = 0.38,20% above 0.50;σ = ?

the lowest 4%

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by N(50,6).Draw and label the Normal model.About what percent represents snowfall of less than 62 cm?

On a recent English exam,scores averaged 84 points.If 41% of scores fell below 70 points,find an approximate standard deviation (assuming the Normal model is appropriate).

The freethrow percentages for the participants of a basketball tournament were compiled.The percents ranged from 40% to 96% with a mean of 53% and a standard deviation of 8%.The quartiles and median percentages were 50%,84%,and 53%.This year's tournament percentages are 3% higher than last year's tournament percentages.Find last year's tournament mean,median,and standard deviation of the freethrow percentages.

A salesman's commission averages $23,700 per year.Last year his commission was $18,900 which corresponded to a z-score of -1.2.Find the standard deviation.

The average number of average number of hours per day a university student spends on homework is 5 hours with a standard deviation of 1.25 hours.How many standard deviations from the mean is 2 hours spent on homework?

Based on the Normal model for snowfall in a certain town N(57,8),how many cm of snow would represent the 75th percentile?

Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 129 minutes,mean = 79 minutes,median = 79 minutes,range = 99 minutes,IQR = 64,Q1 = 32,standard deviation = 11 minutes.Suppose last year's race results were better by 8%.Find last year's mean and standard deviation.Express your answer in exact decimals.

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 140 grams to 305 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 148,246,and 202 grams.Find the range and IQR of the weights.