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

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?

-0.73 < z < 2.27

The speed vehicles traveled on a local road was recorded for one month.The speeds ranged from 48 km/h to 63 km/h with a mean speed of 57 km/h and a standard deviation of 6 km/h.The quartiles and median speeds were 51 km/h,60 km/h,and 54 km/h.Suppose increased patrols reduced speeds by 7%.Find the new mean and standard deviation.Express your answer in exact decimals.

For a recent English exam,use the Normal model N(73,9.2)to find the percent of scores between 56 and 87.Round to the nearest tenth of a percent.

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?

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 highest 15% of the speeds?

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?

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.

Here are some summary statistics for the size of forest fires last year: smallest $\text { fire } = 92$ acres, $\text { mean } = 462$ acres, $\text { median } = 462$ acres, $\text { range } = 7908$ acres, $\mathrm { IQR } = 375 \text {, }$ $Q 1 = 185 \text {, }$ standard $\text { deviation } = 57$ acres.If it costs $1200 per acre to fight the fires,find the minimum,median,standard deviation,and IQR of the cost.

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?

the lowest 96%