Mathematics, 05.02.2020 10:51, jeremiah1212

Agrocery store will only accept yellow onions that are at least 2.75 in. in diameter. a grower has a crop of onions with diameters that are normally distributed, with a mean diameter of 3.25 in. and a standard deviation of 0.25 in. what percent of the onions will be accepted by the grocery store?

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Imagine (or draw) a standard normal curve. Draw a vertical line through the center of this curve, and mark it 3.25 inches. This is the mean diameter. Next, draw vertical lines to represent these sums: 3.25 plus .25, or 3.50 inches; 3.25 less .25, or 3.00 inches, and 3.25 less .50 inches, or 2.75 inches.

Note that 2.75 inches is 2 standard deviations below the mean: That's 2.75 inches less twice 0.25 inches, or 2.75 = 3.25 inches less 2(0.25) inches.

onions with diameters less than 2.75 are rejected; onions with diameters greater than 2.75 inches are accepted.

Find the area to the LEFT of 2.75 inches. In other words, find the area to the left of 2 standard deviations below the mean.

I would use the Empirical Rule here: "68% of data is within 1 standard dev. of the mean; 95% is within 2 standard dev. of the mean.

This tells us that the area to the left of 2.75 inches or -2 standard deviations is 0.025 (half of 0.050). Subtract this from 1.000; you'll get 0.975. This means that 97.5% of the onions will prove to be acceptable, whereas 2.5% will be rejected because they are less than 2.75 inches in diameter.

You could also use a table of z-scores to do this: Determine from the table the area under the std. normal curve to the left of -2 std. dev. Again, this comes out to 0.025, meaning that the area to the right of -2 std. dev is 0.975.

answered: Guest

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

answered: Guest

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000