Asked Jan 16, 2020

Outliers For the purposes of constructing modified boxplots as described in Section 3–4, outliers are defined as data values that are above q3 by an amount greater than 1.5 × IQR or below q1 by an amount greater than 1.5 × IQR, where IQR is the interquartile range. Using this definition of outliers, find the probability that when a value is randomly selected from a normal distribution, it is an outlier.


Expert Answer

Step 1

The values Q1 and Q3 represent the first and third quartile.

Generally the probability values of first quartile Q1 and third quartile Q3 are 0.25 and 0.75, respectively.

Step 2

Use Standard normal (z) distribution table to find the z scores.


For the area to the left of 0.25,

  • Locate the nearest value of 0.25 in the body of the Table.
  • Move left until the first column and note the value as –0.6.
  • Move upward until the top row and note the value as 0.07.

Thus, the z score for Q1 is –0.67.


For the area to the left of 0.75,

  • Locate the nearest value of 0.75 in the body of the Table.
  • Move left until the first column and note the value as 0.6.
  • Move upward until the top row and note the value as 0.07.

Thus the z score for Q3 is 0.67.

The formula to find the interquartile range IQR is,

Statistics homework question answer, step 2, image 1
Step 3

The outlier values that are above Q3 by an amount ...

Statistics homework question answer, step 3, image 1

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Advanced Topics in Statistics

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: Mendel’s Peas Mendel conducted some his famous experiments with peas that were either smooth yellow ...

A: Combination Rule:There are n different items and r number of selections and if the selections are ma...


Q: Women Who Give Birth An epidemiologist plans to conduct a survey to estimate the percentage of women...

A: a)


Q: Birth Weights Based on Data Set 4 “Births” in Appendix B, newborn males have weights with a mean of ...

A: z score for the male:Let X be the weight for newborn males.The formula for the z score is,


Q: In each of Exercises, we have presented either a contingency table or a joint probability distributi...

A: The formula for conditional probability is,


Q: Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a...

A: The test score z between 1.50 and 2.50 is obtained by finding the difference between the areas to th...


Q: Simulating Dice When two dice are rolled, the total is between 2 and 12 inclusive. A student simulat...

A: Consider the experiment of rolling two dice. There are 36 equally likely outcomes. The sum of the nu...


Q: Seat Designs. In Exercises 13–20, use the data in the table below for sitting adult males and female...

A: The random variable x represents the back-to-knee length of males.The length that separates the bott...


Q: Brand Recognition In a study of brand recognition of Sony, groups of four consumers are interviewed....

A: Requirements:The following requirements should be satisfied for the distribution to follow the proba...


Q: Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug zopiclone fo...

A: One sample t test:Here, n is 16, x-bar is 98.9 and s is 42.3Since population standard deviation is n...