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The mean of a normal probability distribution is 380; the standard deviation is 55. Refer to...

The mean of a normal probability distribution is 380; the standard deviation is 55. Refer to the table in Appendix B.1. (Round the final answers to 2 decimal places.)   

a. About what percentage of the observations lie between 325 and 435?

Percentage of observations            %

b. About what percentage of the observations lie between 270 and 490?

   

Percentage of observations            %

c. About what percentage of the observations lie between 215 and 545?

   

Percentage of observations            %

Math   Statistics-And-Probability   
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Answer #1

According to empirical rule, 68%, 95% and 99.7% of data lies within 1, 2 and 3 standard deviations of mean respectively.

Mean = 380

Standard deviation = 55

a) 380 - 1x55 = 325

380 + 1x55 = 435

325 to 435 is within 1 standard deviation of mean.

About what 68% of the observations lie between 325 and 435

b) 380 - 2x55 = 270

380 + 2x55 = 490

270 to 490 is within 2 standard deviations of mean.

About what 95% of the observations lie between 270 and 490

c) 380 - 3x55 = 215

380 + 3x55 = 545

215 to 545 is within 3 standard deviations of mean.

About what 99.7% of the observations lie between 215 and 545

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