A square has an area of 144m^2 What is the length of each side?

An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made t

solniwko [45]

Answer:

B) Method 2 will increase the standard deviation of the students' scores.

Step-by-step explanation:

Given that an instructor in a college class recently gave an exam that was worth a total of 100 points.

The average score for his students was 43 and the standard deviation of the scores was 5 points.

And now he is considering two different strategies for rescaling the exam results of which:

Method 1 = Add 17 points to everyone's score.

Method 2 = Multiply everyone's score by 1.7 .

And we have to check what will be the impact of these methods on the standard deviation of the students' scores.

For this let us consider a simple example to understand this:

Firstly, Formula for calculating Standard Deviation = $\sqrt{\frac{\sum (X-Xbar)^{2}}{n-1}}$

Suppose,

X X - Xbar $(X - Xbar)^{2}$

3 3 - 6 = -3 -3 * -3 = 9

5 5 - 6 = -1 -1 * -1 = 1

10 10 - 6 = 4 4 * 4 = 16

Mean of above data, Xbar = $\frac{3+ 5+10}{3}$ = 6

Standard Deviation of data = $\sqrt{\frac{26}{3-1} }$ = 3.6055

Now let us suppose that we multiply each value of above data with 2 so the new data will be:

X X - Xbar $(X - Xbar)^{2}$

3*2 = 6 6 - 12 = -6 -6 * -6 = 36

5*2 = 10 10 - 12 = -2 -2 * -2 = 4

10*2 =20 20 - 12 = 8 8 * 8 = 64

Mean of new data, Xbar = $\frac{6+ 10+20}{3}$ = 12

Standard Deviation of new data = $\sqrt{\frac{104}{3-1} }$ = 7.2111

Hence, we see that when we multiply any value to the data the standard deviation will increase and in other words it will multiplied by that value which value we multiplied with each data value i.e. when we multiply each data value with 2 the standard deviation also get multiplied by as

3.6055 * 2 = 7.2111

Therefore option B is correct that Method 2 will increase the standard deviation of the students' scores.

And on the other hand Similarly by adding any constant to the data the Standard Deviation will remain same. Therefore Method 1 will have no impact on standard deviation of the students' scores.

8 0

4 years ago

One school purchased 16 gallons of blue paint to decorate several of its classrooms. If

Elodia [21]

Answer: zero

Explanation: if one classroom on its own needed 17 gallons of paint and they only purchased 16,-- which is less than needed for one classroom- how would there be enough for any other classroom?

4 0

3 years ago

A researcher asks random samples of residents of two separate counties as to whether they had purchased organically grown food i

Leni [432]

Answer:

2 proportions z test

The two populations are named as residents from the first county and residents from the second county.

Step-by-step explanation:

This is testing hypothesis about the difference between two proportions.

When the proportions are tested if they are the test statistic

z= ( p^1-p^2)- (p1-p2) / √p₁q₁/n₁ + p₂q₂/ n₂

where p^1 is the proportion of success in the first sample and p^2 of size n₁ is the proportion of success in the second sample of size n₂ with unknown proportions of successes p1 and p2 respectively.

When the sample sizes are sufficiently large

z= ( p^1-p^2)- (p1-p2) / √p₁q₁/n₁ + p₂q₂/ n₂ is approximately standard normal.

The two populations are named as residents from the first county and residents from the second county.

7 0

3 years ago

A pizza box measure 16 inches by 16 inches by 2 inches .what is the volume of the box?

OverLord2011 [107]

V= L x w x h

V= 16 x 16 x 2

V= 256 x 2

V=512 inches

4 0