Question

The area covered by a normal distribution curve from 3 sigma to + 3 sigma?

Answer 1

Answer:

The area covered by a normal distribution curve from 3 sigma to + 3 sigma is 99.7%.

Step-by-step explanation:

Let the random variable X follow a Normal distribution with mean μ and standard deviation σ.

According to the Empirical rule all the observations of a normal distribution will fall within three standard deviations of the mean. Or more specifically:

• 68% of the observations fall within one standard deviations of the mean, i.e.  $P(\mu+\sigma\leq X\leq \mu-\sigma)=0.68$

• 95% of the observations fall within two standard deviations of the mean, i.e.  $P(\mu+2\sigma\leq X\leq \mu-2\sigma)=0.95$

• 99.7% of the observations fall within three standard deviations of the mean, i.e.  $P(\mu+3\sigma\leq X\leq \mu-3\sigma)=0.997$

Then the area under a normal curve from - 3σ to + 3σ is 99.7%.

Answer 2

Answer:

99.73% for area covered under -3 sigma to 3 sigma