Question

A normally distributed data set has a mean of 0 and a standard deviation of 2. Which of the following is closest to the percent of values between -4.0 and 2.0?
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Answer 1

A normally distributed data set has a mean of 0 and a standard deviation of 2. The closest to the percent of values between -4.0 and 2.0 would be 84%.

What is the empirical rule?

According to the empirical rule, also known as the 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95%, and 99.7% of the values lies within one, two, or three standard deviations of the mean of the distribution.

$P(\mu - \sigma < X < \mu + \sigma) \approx 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%$

A normally distributed data set has a mean of 0 and a standard deviation of 2.

$Z=(x-\mu)/\sigma$

$P(x=-0.4)\\\\z=(-0.4-0)/2\\\\= -0.2\\\\P(x=2)\\z=(2-0)/2\\\\=1$

$P(-0.4 < x < 2)=p(-0.2 < z < 1)=p(-0.2 < z < 0)+p(0 < z < 1)$……….(by symmetry)

=.49865+.3413

.83995…….(by (http://83995…….by) table value)

=.8400 × 100

=84%

Learn more about the empirical rule here:

brainly.com/question/13676793

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