Please explain 1 Use the 6895997 Rule to find the area unde

Please explain :)

1. Use the 689599.7 Rule to find the area under the Normal distribution for each of the following
regions.
a) Between – 1 and + 2
b) Between – 3 and + 2
c) To the right of + 2
d) To the left of + 2
e) To the left of –

Solution

Note that the 68-95-99.7 rule can also be said that 34-47.5-49.85 percent lie within 1,2, or 3 standard deviations on either side of the mean.

Thus,

a)

34% + 47.5% = 81.5% [ANSWER]

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b)

49.85% + 47.5% = 97.35% [ANSWER]

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c)

50% of data lie on right of the mean. Thus, to the right of u + 2sigma is

50% - 47.5% = 2.5% [ANSWER]

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d)

This is the complement of part c,

100% - 2.5% = 97.5% [ANSWER]

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e)

50% of data lie on the left of the mean. Thus, to the left of u - sigma is

50% - 34% = 16% [ANSWER]