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

Here are some summary statistics for the size of forest fires last year: smallest fire = 72 acres,mean = 493 acres,median = 493 acres,range = 7,928 acres,IQR = 370,Q1 = 197,standard deviation = 59 acres.Between what two values are the middle 50% of fire sizes found?

On a recent English exam,if 20% of scores fell below 60 points and the standard deviation is 7.5,find the mean score (assuming the Normal model is appropriate).

μ = 30,37% below 20;σ = ?

After increased patrol,91% of vehicles on a road travel above 45 km/h with a standard deviation of 5.2 km/h.Assuming a Normal model is appropriate,find the mean speed.

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest amount = 19 cm,mean = 47 cm,median = 40 cm,range = 81 cm,IQR = 54,Q1 = 19,standard deviation = 10 cm.Suppose snowfall was tracked for 5 additional years and the annual snowfall was found to increase by 20%.Find the new mean and standard deviation.

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg.Draw and label the Normal model for systolic blood pressure.What percentage of 18-year-old women have a systolic blood pressure between 96 mm Hg and 144 mm Hg?

z > 0.59

For a recent English exam,use the Normal model N(73,9.2)to find the score that represents the 90th percentile.

On a recent English exam,if 94% of scores fell above 65 points and the standard deviation is 7.5,find the mean score (assuming the Normal model is appropriate).

σ = 16,20% below 100;μ = ?

The mean test score on a statistics test was 72 with a standard deviation of 10.How many standard deviations from the mean is a test score of 90?

μ = 300,90% below 500;σ = ?

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 lowest 96%

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.

After increased patrol,cars on a road travel at speeds averaging 54 km/h.If 10% of vehicles travel above 70 km/h,what approximate standard deviation could represent this model (assuming a Normal model is appropriate)?

Adam played golf on Saturday and Sunday.He scored 82 both days.The scores of all golfers Saturday averaged 68 with a standard deviation of 17.The scores on Sunday averaged 81 with a standard deviation of 9.On which day did Adam do better compared with the other golfers? Explain.

The volumes of soda in 1 litre cola bottle can be described by a Normal model with a mean of 0.95 L and a standard deviation of 0.04 L.What percentage of bottles can we expect to have a volume less than 0.94 L?

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.

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest amount = 19 cm,mean = 40 cm,median = 33 cm,range = 81 cm,IQR = 45 cm,Q1 = 16 cm,standard deviation = 11 cm.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.