Normal Distribution Statistics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

hard
Birth weights are normally distributed with ฮผ=3.5\mu = 3.5 kg and ฯƒ=0.5\sigma = 0.5 kg. What percentage of babies weigh between 2.5 and 4.5 kg?

Solution

  1. 1
    Step 1: 2.5=3.5โˆ’2(0.5)2.5 = 3.5 - 2(0.5), so 2.5 kg is 2 standard deviations below the mean.
  2. 2
    Step 2: 4.5=3.5+2(0.5)4.5 = 3.5 + 2(0.5), so 4.5 kg is 2 standard deviations above the mean.
  3. 3
    Step 3: By the 68-95-99.7 rule, approximately 95% of data falls within 2 standard deviations.

Answer

Approximately 95%.
The 68-95-99.7 rule extends to 2ฯƒ (95%) and 3ฯƒ (99.7%). This is widely used in medical and quality-control applications to define normal ranges.

About Normal Distribution

The normal distribution (bell curve) is a symmetric, bell-shaped probability distribution where most data clusters around the mean, with probabilities decreasing symmetrically toward the tails. It is defined by two parameters: the mean and the standard deviation.

Learn more about Normal Distribution โ†’

More Normal Distribution Examples

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Example 4 medium

A normal distribution has mean [formula] and standard deviation [formula]. Using the 68-95-99.7 rule

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