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A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. Teh mean is 73, wit

zavuch27 [327]

Answer:

The bottom for an A is 75. Round to the nearest whole number as needed.

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the scores on this case, and for this case we know the distribution for X is given by:

$X \sim N(\mu=73,\sigma=7)$

And let $\bar X$ represent the sample mean, the distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

2) The bottom for an A is _____. Round to the nearest whole number as needed.

And we want the top 5.5% of the scores, so we need a value a such that:

$P(X>a)=0.055$ or $P(X$

We need on the right tail of the distribution a value a that gives to us 94.5% of the area below and 5.5% of the area above. Both conditions are equivalent.

Let's use the condition $P(X$ , the best way to solve this problem is using the z score with the following formula:

$z=\frac{x-\mu}{\sigma}$

So we need a value from the normal standard distribution that accumulates 0.945 of the area on the left and 0.055 on the right. This value on this case is 1.598 and we can founded with the following code in excel:

"=NORM.INV(0.945,0,1)"

If we apply the z score formula to our case we have this:

$P(X$

So then based on the equalities we have this:

$\frac{a-73}{7}=1.598$

And if we solve for a we got:

$a=(7*1.598) +73=84.186$

So then we need a score of 84.186 rounded to the nearest whole number 75 or higher in order to get an A

8 0

3 years ago

A bakery makes 4 dozen raisin muffins and 8 dozen blueberry muffins. A dozen is 12 muffins.

swat32

Answer:

144

Step-by-step explanation:

8x12 = 96 and 4x12= 48 and 96+48= 144

7 0

2 years ago

Let f be a twice-differentiable function for all real numbers x. Which of the following additional properties guarantees that f

Mkey [24]

Answer:

(C) f’(c) = 0 and f”(c) > 0

Step-by-step explanation:

A minimum occurs where the first derivative is 0 (the tangent line is horizontal), and the second derivative is positive (concave up). The simplest example of this is a positive parabola, like y = x², which has a relative minimum at its vertex.

8 0

2 years ago

A rectangular package sent by a postal service can have a maximum combined length and girth (perimeter of a cross sectio) of 108

Morgarella [4.7K]

Answer:

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

Step-by-step explanation:

This is a optimization with restrictions problem.

The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).

This restriction can be expressed as:

$4x+L=108$