Estimating Proportions from Normal Distribution: Steps 1-2
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Questions and Answers

What proportion of men aged 18-24 are too small for size medium clothes?

  • 0.4315 (43.15%)
  • 0.5000 (50.00%)
  • 0.3446 (34.46%) (correct)
  • 0.2500 (25.00%)

What is the correct method to find the probability of x < 69 in this scenario?

  • Use only Table A
  • Do manual calculations using z-scores
  • Use R for accurate calculations (correct)
  • Use the 68-95-99.7% rule

What does the text suggest about using z-scores with more than 2 decimal places?

  • R provides more accurate results for z-scores with more than 2 decimal places (correct)
  • Z-scores with more than 2 decimal places should be rounded off
  • Z-scores with more than 2 decimal places are accurate for Table A
  • Table A is better for z-scores with more than 2 decimal places

Why is it mentioned that approximating the proportion for >74 using 68-95-99.7% underestimates the proportion?

<p>Because the rule is too conservative for values above 74 inches (C)</p> Signup and view all the answers

When should the 68-95-99.7% rule be used according to the text?

<p>Only when X falls on a multiple of 1 standard deviation from the mean (A)</p> Signup and view all the answers

What difference is highlighted between R and Table A in the text?

<p>Table A is preferable for z-scores up to 2 decimal places (A)</p> Signup and view all the answers

Which step involves identifying the specific problem and interval of interest?

<p>Step 1: Identify the problem (C)</p> Signup and view all the answers

If the 68-95-99.7% rule cannot be used, which method is recommended for finding the shaded area under the curve (AUC)?

<p>Use R or z-scores and Table A from the textbook (B)</p> Signup and view all the answers

What is the purpose of Step 5: State the solution?

<p>To put the answer in the context of the original question (D)</p> Signup and view all the answers

If the interval of interest is within 1 standard deviation of the mean, which rule can be used to approximate the proportion?

<p>The 68-95-99.7% rule (B)</p> Signup and view all the answers

What is the purpose of Step 3: Draw the distribution?

<p>To visualize the problem and identify the shaded region (C)</p> Signup and view all the answers

Which step involves using statistical software or tables to find the shaded area under the curve?

<p>Step 4: Find the shaded area under the curve (AUC) (B)</p> Signup and view all the answers

Which method can be used to find the z-score corresponding to a given proportion?

<p>Both methods (a) and (b) (A)</p> Signup and view all the answers

What is the equation used to convert from z-score back to the original scale?

<p>$x = \mu + z-score * \sigma$ (D)</p> Signup and view all the answers

What is the interval of heights that falls between 2 and 3 standard deviations above the mean for men aged 18-24 with a normal distribution of N(70, 2.5) inches?

<p>[75, 77.5] (A)</p> Signup and view all the answers

What proportion of men have heights between 2 and 3 standard deviations above the mean, according to the 68-95-99.7% rule?

<p>4.15% (C)</p> Signup and view all the answers

Which of the following is NOT a benefit of using the qnorm() function in R to find z-scores?

<p>It requires less statistical knowledge to use (B)</p> Signup and view all the answers

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