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Part 1
In a survey 100 people were asked to pick a number from 1 to 5. The results are tabulated below.
Number Chosen
1
2
3
4
5
Number Who Chose
That Number
15
26
21
22
16
​a) What is the probability that the number chosen is​ 1? 2?​ 3? 4?​ 5?
​b) What general conclusion might be made from the results of the​ experiment?
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Part 1
​a) What is the probability that the number chosen is​ 1?
  
. 15
Part 2
What is the probability that the number chosen is​ 2?
  
. 26
Part 3
What is the probability that the number chosen is​ 3?
  
. 21
Part 4
What is the probability that the number chosen is​ 4?
  
. 22
Part 5
What is the probability that the number chosen is​ 5?
  
. 16
Part 6
​b) Choose the correct answer below.
A.
People tend to pick the greatest number.
B.
People tend not to pick the least or greatest numbers.
C.
People tend to pick the least number.
D.
People tend not to pick the middle numbers.

1 answer

To calculate the probability of each number chosen, we can use the formula for probability:

\[ P(\text{number}) = \frac{\text{Number Who Chose That Number}}{\text{Total Number of People Surveyed}} \]

In this case, the total number of people surveyed is 100.

Part 1: Probability Calculations

  • Probability that the number chosen is 1: \[ P(1) = \frac{15}{100} = 0.15 \]

  • Probability that the number chosen is 2: \[ P(2) = \frac{26}{100} = 0.26 \]

  • Probability that the number chosen is 3: \[ P(3) = \frac{21}{100} = 0.21 \]

  • Probability that the number chosen is 4: \[ P(4) = \frac{22}{100} = 0.22 \]

  • Probability that the number chosen is 5: \[ P(5) = \frac{16}{100} = 0.16 \]

Summary of Probabilities:

  • \( P(1) = 0.15 \)
  • \( P(2) = 0.26 \)
  • \( P(3) = 0.21 \)
  • \( P(4) = 0.22 \)
  • \( P(5) = 0.16 \)

Part 2: General Conclusion

To draw a conclusion from the probabilities, we compare the likelihood of choosing different numbers.

The results indicate:

  • The number 2 was chosen the most frequently (26 choices), indicating a preference towards the lower middle numbers.
  • The numbers 1 and 5 were chosen the least frequently, suggesting that extremes (the lowest and highest numbers) were not favored.

Conclusion Options Evaluation

  • A. People tend to pick the greatest number. (Incorrect — number 5 had the least frequency.)
  • B. People tend not to pick the least or greatest numbers. (Seems accurate since numbers 1 and 5 have the lowest frequencies.)
  • C. People tend to pick the least number. (Incorrect — number 1 had a low frequency.)
  • D. People tend not to pick the middle numbers. (Incorrect — middle numbers, particularly, 2, 3, and 4, had higher frequencies.)

Given the observations, the correct answer is B. People tend not to pick the least or greatest numbers.