17 Questions
What proportion of men aged 18-24 are too small for size medium clothes?
0.3446 (34.46%)
What is the correct method to find the probability of x < 69 in this scenario?
Use R for accurate calculations
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
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
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
What difference is highlighted between R and Table A in the text?
Table A is preferable for z-scores up to 2 decimal places
Which step involves identifying the specific problem and interval of interest?
Step 1: Identify the problem
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
What is the purpose of Step 5: State the solution?
To put the answer in the context of the original question
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
What is the purpose of Step 3: Draw the distribution?
To visualize the problem and identify the shaded region
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)
Which method can be used to find the z-score corresponding to a given proportion?
Both methods (a) and (b)
What is the equation used to convert from z-score back to the original scale?
$x = \mu + z-score * \sigma$
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]
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%
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
Learn the steps for estimating proportions from a normal distribution, focusing on questions 1 and 2. Understand how to determine the percentage of individuals within a specified interval using the known population mean and standard deviation.
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