Math Problem Statement

A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of 10 corn plants. He labels the 100 plants 00–99. Refer to the given line from a random number table. Which numbers represent the sample of 10 corn plants?

58160 09695 38399 40400 32662 46254

58, 16, 00, 96, 95, 38, 39, 94, 04, 00 58, 16, 00, 96, 95, 38, 39, 94, 04, 32 58, 16, 96, 95, 38, 39, 94, 04, 32, 66 58, 16, 09, 69, 38, 39, 40, 32, 66, 46

Solution

To determine the correct sample of 10 corn plants from the random number table, we interpret the numbers in groups of two digits (since the plants are labeled 00–99). Numbers are selected sequentially, skipping any duplicates or numbers outside the range (00–99).

Random number table:
58160 09695 38399 40400 32662 46254

  • Step-by-step grouping into pairs of two digits:
    • 58, 16, 00, 09, 69, 38, 39, 40, 32, 66, 24

These numbers are all within the range 00–99 and contain no duplicates.

Thus, the sample of 10 corn plants is:
58, 16, 09, 69, 38, 39, 40, 32, 66, 46

The correct answer is:
58, 16, 09, 69, 38, 39, 40, 32, 66, 46


Do you want further clarification on the method used to interpret the random number table?

Here are 5 related questions for deeper understanding:

  1. What is the concept of simple random sampling and how does it work?
  2. How do random number tables ensure fairness in sampling?
  3. Can duplicates in the random numbers affect the outcome of a sample? Why?
  4. How are random number generators used in place of random number tables?
  5. What are other ways farmers could estimate yields using sampling methods?

Tip: Always skip numbers in a random table that are outside the desired range or duplicate an earlier selection in simple random sampling.

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Math Problem Analysis

Mathematical Concepts

Statistics
Simple Random Sampling
Random Number Generation

Formulas

None (involves concept-based grouping of numbers)

Theorems

Basic principles of randomness and sampling in statistics

Suitable Grade Level

Grades 9-12