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Probability Calculation with Sampling Distribution: Left-Handed Students Seating Issue

Calculate the probability of not enough seats for left-handed students in a class of 90, based on a population proportion of 13%. Apply sampling distribution concepts to solve the problem and understand z-scores.

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Probability Calculation with Sampling Distribution: Left-Handed Students Seating Issue

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  1. Chapter 18 Sampling Distribution

  2. Key Concepts SD( p) =

  3. Example 1 • Suppose that about 13% of the population is left handed. A 200 seat school auditorium has been built with 15 lefty seats. In a class of 90 students what is the probability that there will not be enough seats for the left handed students?

  4. Plan • We want the probability of finding more that 16.7% left handed students out of a sample size of 90 students if the proportion of lefties is 13%.

  5. Always check conditions • Randomization Condition: • 10% condition: • Success/ Failure np>10 nq > 10

  6. State the parameter and the sampling distribution model • p= • The conditions are satisfied N( mean ( use population proportion), SD) N(.13, .035)

  7. Draw it

  8. Find the z-score z= P( p >.167) =

  9. Example 2 • Information on a packet of seeds claims that the germination rate is 92%. What is the probability that more than 95% of the 160 seeds in the packet will germinate?

  10. Plan

  11. Conditions

  12. State the parameter and the sampling distribution model • p= • The conditions are satisfied N( mean ( use population proportion), SD) N( )

  13. Plot it

  14. z score

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