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 IQR?

The average number of babies born in a certain town each year is 218 with a standard deviation of 26.How many standard deviations from the mean is a year with 387 babies born?

Based on the Normal model for snowfall in a certain town N(57,8),how many cm of snow would represent the 25th percentile?

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).

-0.55 < z < 0.55

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?

σ = 0.01,2.28% below 0.32; μ = ?

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).

Based on the Normal model for car speeds (in km/h)on a road N(77,9.1),what are the cutoff values for the middle 20% of the speeds?

z < 1.13

Here are some statistics for the annual Wildcat golf tournament: lowest $\text { score } = 58 \text {, }$ mean $\text { score } = 95 \text {, }$ median = 103,range = 92,IQR = 110, $\mathrm { Q } 1 = 38 \text {, }$ standard $\text { deviation } = 15 \text {. }$ 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.

A bank's loan officer rates applicants for credit.The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50.If an applicant is randomly selected,what percentage can be expected to be between 200 and 275?

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?

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

For a recent English exam,use the Normal model N(73,9.2)to find the percent of scores under 58.Round to the nearest tenth of a percent.

The annual snowfall in a town (in cm)can be represented by the Normal model N(45,7.1).What amount of snowfall would you expect to be unusually high for this town?

The average amount of sugar a person eats per year is 4 kg.A person who consumes 3.25 kg of sugar has a z-score of -0.75.Find the standard deviation.

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 setter on your school's volleyball team averages 58 assists per match with a standard deviation of 6.How many standard deviations from the mean is an outing with 79 assists?