Estimating Proportions from Normal Distribution: Steps 1-2

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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?

Because the rule is too conservative for values above 74 inches Signup and view all the answers

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

Only when X falls on a multiple of 1 standard deviation from the mean Signup and view all the answers

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

Table A is preferable for z-scores up to 2 decimal places Signup and view all the answers

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

Step 1: Identify the problem 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)?

Use R or z-scores and Table A from the textbook Signup and view all the answers

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

To put the answer in the context of the original question 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?

The 68-95-99.7% rule Signup and view all the answers

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

To visualize the problem and identify the shaded region Signup and view all the answers

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

Step 4: Find the shaded area under the curve (AUC) Signup and view all the answers

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

Both methods (a) and (b) Signup and view all the answers

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

$x = \mu + z-score * \sigma$ 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?

[75, 77.5] 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?

4.15% 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?

It requires less statistical knowledge to use Signup and view all the answers

Estimating Proportions from Normal Distribution: Steps 1-2

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