On his last test, Bernice\'s test grade was in the top 8% of students. If the me

Question

On his last test, Bernice's test grade was in the top 8% of students. If the mean of the grades was 79 with a standard deviation of 4.3, what was the minimum score Bernice could have made? 6. The thorax lengths in a population of male fruit flies follow a Normal distribution with mean 0.800 millimeters (mm) and standard deviation 0.078 mm. What are the median and the first and third quartiles of thorax length? 7.The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches. Men the same age have mean height 69.3 inches with standard deviation 2.8 inches. What are the z-scores for a woman 6 feet tall and a man 6 feet tall? Say in simple language what information the z-scores give that the actual heights do not. 8. Find the z score such that 62% of the observations fall above Z. 9. In its Fuel Economy Guide for 2008 model vehicles, the Environmental Protection Agency gives data on 1152 vehicles. There are a number of outliers, mainly vehicles with very poor gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other 1120 or so vehicles is approximately Normal with mean 18.7 miles per gallon (mpg) and standard deviation 4.3 mpg. How high must a 2008 vehicle's gas mileage be in order to fall in the top 10% of all vehicles? (Outliers omitted)

Explanation / Answer

5)

P(X>x) = 0.08 Where x is the score obtained

Mean = 79

SD = 4.3

Z= (X-Mean)/SD

We know that the score is in top 8% which means that P(Z<z) = 0.92

(X-79)/4.3 = 1.41

X= 85.06

His score must be >= 85.06

9)

n= 1120

Mean = 18.7

SD = 4.3

P(Z<z) = 0.9

(X-18.7)/4.3/sqrt(1120) = 1.29

X= 18.86

Mileage should be greater than 18.86 to be in top 10% of all vehicles

Hope this helps :)

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