Question

Use the empirical rule (68-95-99.7) to determine if the following maximum
daily rainfall totals could be considered to be normally distributed.
1.1, 1.2, 1.5, 1.55, 1.71, 1.75, 1.9, 1.94, 1.99, 2.0, 2.05, 2.08, 2.12, 2.18, 2.2,
2.25, 2.36, 2.5, 2.61, 2.81, 2.88, 2.95, 3.0, 3.03, 3.07, 3.16, 3.25, 3.62.
please help I don't understand this problem at all

Answer 1

well, i would assume we want to start with the mean and standard deviation of the set

Answer 2

so the mean is 2.3 and the standard deviation would be 2.9, I think? @amistre64

Answer 3

{1.1, 1.2, 1.5, 1.55, 1.71, 1.75, 1.9, 1.94, 1.99, 2.0, 2.05, 2.08, 2.12, 2.18, 2.2, 2.25, 2.36, 2.5, 2.61, 2.81, 2.88, 2.95, 3.0, 3.03, 3.07, 3.16, 3.25, 3.62}

mean of 2.3 is fine .. but your deviation is off according to the wolf

Answer 4

mean +- 1sd gives us the normal spread about the mean for 68% of the data.

+- 2 sd and +- 3 sd give us the spreads for the other rule parts.

I would say that if that much of the data is approximately in the spread, then its good

Answer 5

when i graphed it out as a normal distribution on a graphing calculator, it looked like a normal distribution. So because most values are grouped around the mean, in the 68% would be explaing that the data is a normal distribution?

Answer 6

@Amistre64

Answer 7

im not sure about that approach, but then im not grading it.

'it looks like' is not a very sound approach to me.

Answer 8

in a normal distribution, approximatly 68% of the data is within 1 standard deviation of the mean ... i do not see that process being done very well by 'it looks like'

Answer 9

I just can't think of any other way to explain how to use the 68,95,99.7 empirical rule to explain if a set of data is normally distributed. @amistre64

Answer 10

1.1, 1.2, 1.5, 1.55, 1.71, 1.75, 1.9, 1.94, 1.99, 2.0, 2.05, 2.08, 2.12, 2.18, 2.2, 2.25,

mean = 2.3 or so
sd = .64 or something like it

2.36, 2.5, 2.61, 2.81, 2.88, 2.95, 3.0, 3.03, 3.07, 3.16, 3.25, 3.62

mean +- 1 sd

2.3 + .64 = 2.97
2.3 - .64 = 1.66

1.71, 1.75, 1.9, 1.94, 1.99, 2.0, 2.05, 2.08, 2.12, 2.18, 2.2, 2.25, 2.36, 2.5, 2.61, 2.81, 2.88, 2.95

18 out of 28 = 18/28 = .6428, or about 64.3% of the data, which may be close enough to 68% for comparisons.

try it at +- 2sd and see what you get

Answer 11

the only way i can see to use the rule, is to define how much data lies within the required number of standard deviations ....

Answer 12

it looks like almost all the data except for one value is between -2 and 2 or at least that's what im getting. @amistre64

Answer 13

youve got 28 data points

.68(28) = 19.04, so about 19 or 20 data points should be about the mean within +-1 sd

.95(28) = 26.6, so about 26 or 27 data points should be about the mean within +- 2 sd

etc ...

Answer 14

1.472 to 3.58

1.5, 1.55, 1.71, 1.75, 1.9, 1.94, 1.99, 2.0, 2.05, 2.08, 2.12, 2.18, 2.2, 2.25, 2.36, 2.5, 2.61, 2.81, 2.88, 2.95, 3.0, 3.03, 3.07, 3.16, 3.25

25 data points, is close to 26 or 27 yes

Answer 15

assuming the mean and sd chosen is appropriate :)

Answer 16

okay thank you so much that makes much better sense than what i was thinking it was saying :) @amistre64

Answer 17

youre welcome :)