A data set with a mean of 34 and a standard deviation of 2.5 is normally distributed.
According to the Empirical Rule, what percent of the data is in each of the following ranges? Round to the nearest tenth of a percent if necessary.

Between
34 and 39 Less than 31.5 Between
29 and 36.5
Percentage
%
%
%

a) From the mean and 2 deviations above we have 95/2% = 47.5% of the data

b) Below one deviation from the mean we have (50-34)% =16% of the data

c) One deviation below the mean and 2 deviations above we have (47.5%) +34% = 81.5% of the data

Step-by-step explanation:

For this case we know that for a random variable X we have:

The empirical rule states that within one deviation from the mean we have 68% of the values, within 2 deviations 95% and ithin 3 deviations 99.7% of the data.

So then we want to find the % between 34 and 39. We can use the z score formula given by:

In order to calculate the deviations from the mean and replacing we got:

And from the mean and 2 deviations above we have 95/2% = 47.5% of the data

For the probability that would be less than 31.5 we find the z score:

And below one deviation from the mean we have (50-34)% =16% of the data

And for the last part between 29 and 36.5 we find the z scores and we got:

And from one deviation below the mean and 2 deviations above we have (47.5%) +34% = 81.5% of the data

687.09 dollars       happy now

step-by-step explanation: 6870

1857 times .63 equals 1169.91 subtract that from 1857 you get 687.09

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1