Attacking Probability and Statistics Problems by David S. Kahn

Author:David S. Kahn
Language: eng
Format: epub, mobi
Publisher: INscribe Digital
Published: 2016-04-13T04:00:00+00:00

Note how far the maximum value line is from the box relative to the minimum value line. It is customary to define an outlier as a value that is either 1.5 IQR below Q1 or 1.5 IQR above Q3. In Example 7, the IQR = 16 − 7 = 9, and (1.5)(9) = 13.5. Thus, an outlier is a value that is above 16 + 13.5 = 29.5 or below 7 − 13.5 = −6.5. There is one value, 30, that is an outlier.

Time to practice!

Practice Problems

Practice Problem 1: Suppose that the typical 18-year-old man consumes 2300 calories a day, with a standard deviation of 400 calories. Use the Empirical Formula to estimate what percentage of 18-year-old men consume between 1500 and 3100 calories a day?

Practice Problem 2: Suppose that the average age of an American car is now 11.1 years, with a standard deviation of 3.2 years. Use the Empirical Formula to estimate what percentage of cars are of an age between (a) 14.3 years and 7.9 years; (b) greater than 14.3 years?

Practice Problem 3: Given the calorie information in Practice Problem 1, approximately what percentage of 18-year-old men consume between 1100 and 2700 calories a day?

Practice Problem 4: Given the age information in Practice Problem 2, approximately what percentage cars are of an age between 11.1 and 17.5 years?

Practice Problem 5: Given the calorie information in Practice Problem 1, what is the z score for an 18-year-old man who consumes 2550 calories a day?

Practice Problem 6: Given the age information in Practice Problem 2, what is the z score of a car that is 18.2 years old?

Practice Problem 7: In Town A, in a typical 30-day stretch, the mean number of days of rain is 11 with a standard deviation of 4. In Town B, in a typical 30-day stretch, the mean number of days of rain is 22, with a standard deviation of 3. Is it more unusual if Town A has a 30-day stretch with no rain or if Town B has a 30-day stretch where it rains every day?

Practice Problem 8: A typical fish of species X lays a mean number of 3000 eggs with a standard deviation of 220 eggs. A typical fish of species Y lays a mean number of 5000 eggs with a standard deviation of 550 eggs. Is it more unusual for a fish of species X to lay 2300 eggs or for a fish of species Y to lay 7000 eggs?

Practice Problem 9: In Practice Problem 7, how many days in a 30 day stretch would it have to rain in Town A for the number of days to be 2.5 standard deviations above the mean?

Practice Problem 10: In Practice Problem 8, how many eggs would fish Y have to lay to be 1.7 standard deviations below the mean?

Practice Problem 11: Group the following PSAT scores into quartiles. Give the five-number summary of the data:

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