Question 1: Best Measure of Dispersion

The best measure of dispersion is Standard Deviation because it considers all data points and provides a measure of how spread out the values are around the mean.

✅ Correct Answer: (d) Standard deviation

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Question 2: Percentage of Items Between 24 and 44

Given:

• Mean $\mu = 20$
• Variance $\sigma^2 = 64$, so $\sigma = \sqrt{64} = 8$
• We need $P(24 \leq X \leq 44)$

Convert to standard normal form:
$Z = \frac{X - \mu}{\sigma}$ For $X = 24$:
$Z_1 = \frac{24 - 20}{8} = \frac{4}{8} = 0.5$
For $X = 44$:
$Z_2 = \frac{44 - 20}{8} = \frac{24}{8} = 3$

Using the standard normal table:
$P(Z < 0.5) = 0.6915, \quad P(Z < 3) = 0.9987$
$P(0.5 \leq Z \leq 3) = 0.9987 - 0.6915 = 0.3072 = 30.72\%$

✅ Correct Answer: (b) 30.72

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Question 3: Points of Inflexion of Normal Distribution Curve

The points of inflexion of the normal distribution curve occur at:

$x = \mu \pm \sigma$

✅ Correct Answer: (d) $\mu \pm \sigma$

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Would you like a deeper explanation or more examples?

Here are 5 related questions to expand your understanding:

1. What is the difference between variance and standard deviation?
2. Why is standard deviation preferred over range as a measure of dispersion?
3. How is the normal distribution used in real-life applications?
4. What is the empirical rule for normal distribution (68-95-99.7 rule)?
5. How do you compute probability using the standard normal table?

Tip:

For quick probability calculations in a normal distribution, always convert values to Z-scores and use a Z-table to find probabilities! 🚀