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

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 both shoes is 51 km,which shoe would you purchase before starting your marathon training (where you figure to run 500 km)? Explain.

Based on the Normal model for car speeds (in km/h)on a road N(77,9.1),what is the cutoff value for the lowest 30% of the speeds?

z < 1.13

Here are some summary statistics for last year's basketball team scoring output: lowest score = 23 points,mean = 53 points,median = 47 points,range = 92 points,IQR = 51,Q1 = 32,standard deviation = 5 points.Between what two values are the middle 50% of scores found?

The local basketball team averages 65% from the freethrow line.A player who makes 72.5% of his freethrows has a z-score of 1.5.Find the standard deviation.

0.7 < z < 1.98

σ = 0.01,2.28% below 0.32;μ = ?

-1.10 < z < -0.36

-2.41< z < 0

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $15,000,mean salary = $35,000,median = $25,000,range = $60,000,IQR = $30,000,first quartile = $17,500,standard deviation = $20,000. Between what two values are the middle 50% of the salaries found?

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by N(45,7).Draw and label the Normal model.What percent of snowfall is between 52 cm and 59 cm?

The mean weight of babies born in a hospital last year was 2.84 kg.Suppose the standard deviation of the weights is 0.95 kg.Which would be more unusual,a baby weighing 1.8 kg or a baby weighing 3.83 kg? Explain.

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 137 grams to 196 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 151,249,and 202 grams.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

An English instructor gave a final exam and found a mean score of 72 points and a standard deviation of 6.9 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.What percent of scores should be between 85.8 and 92.7 points?

Here are some summary statistics for the size of forest fires last year: smallest fire = 92 acres,mean = 462 acres,median = 462 acres,range = 7,908 acres,IQR = 375,Q1 = 185,standard deviation = 57 acres.If it costs $1200 per acre to fight the fires,find the minimum,median,standard deviation,and IQR of the cost.

A town's average snowfall is 45 cm per year with a standard deviation of 9 cm.Using a Normal model,what values should border the middle 68% of the model?

On a recent English exam,scores averaged 77 points.If 2% of scores fell above 95 points,find an approximate standard deviation (assuming the Normal model is appropriate).

the lowest 9%

The speed vehicles travelled on a local road was recorded for one month.The speeds ranged from 50 km/h to 65 km/h with a mean speed of 55 km/h and a standard deviation of 7 km/h.The quartiles and median speeds were 53 km/h,62 km/h,and 52 km/h.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

the highest 86%