What is the lcm of 24 and 36

2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviati

Ket [755]

Answer:

$\sigma = 11.28$ --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Explain how the standard deviation is calculated.

Start by calculating the mean

To do this, we divide the sum of the products of grade and number of students by the total number of students;

i.e.

$\bar x = \frac{\sum fx}{\sum f}$

So, we have:

$\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}$

$\bar x = \frac{7531}{91}$

$\bar x = 82.76$

Next, calculate the variance using the following formula:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}$

i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset

So, we have:

$\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}$

$\sigma^2 = \frac{11580.6816}{91}$

$\sigma^2 = 127.26$

Lastly, take the square root of the variance to get the standard deviation

$\sigma = \sqrt{\sigma^2}$

$\sigma = \sqrt{127.26}$

$\sigma = 11.28$ --- approximated

Hence, the standard deviation is approximately 11.28

Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.

8 0

3 years ago

1. Mark and Bill have a combined weight of 170

qwelly [4]

<h3>Equation : x + y = 170 and y = 2x - 40</h3><h3>The weight of Bill is 70 pounds and weight of mark is 100 pounds</h3>

Solution:

Let the weight of Bill be "x"

Let the weight of mark be "y"

Given that,

Mark and Bill have a combined weight of 170 pounds

Therefore,

x + y = 170 ------- eqn 1

Mark weighs 40 pounds less than twice Bill's weight

y = 2x - 40 ------- eqn 2

Substitute eqn 2 in eqn 1

x + 2x - 40 = 170

3x = 170 + 40

3x = 210

x = 70

Substitute x = 70 in eqn 2

y = 2(70) - 40

y = 140 - 40

y = 100

Thus weight of Bill is 70 pounds and weight of mark is 100 pounds

6 0

3 years ago

In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data it was noted tha

siniylev [52]

Answer: Probability that students who did not attend the class on Fridays given that they passed the course is 0.043.

Step-by-step explanation:

Since we have given that

Probability that students attend class on Fridays = 70% = 0.7

Probability that who went to class on Fridays would pass the course = 95% = 0.95

Probability that who did not go to class on Fridays would passed the course = 10% = 0.10

Let A be the event students passed the course.

Let E be the event that students attend the class on Fridays.

Let F be the event that students who did not attend the class on Fridays.

Here, P(E) = 0.70 and P(F) = 1-0.70 = 0.30

P(A|E) = 0.95, P(A|F) = 0.10

We need to find the probability that they did not attend on Fridays.

We would use "Bayes theorem":

$P(F\mid A)=\dfrac{P(F).P(A\mid F)}{P(E).P(A\mid E)+P(F).P(A\mid F)}\\\\P(F\mid A)=\dfrac{0.30\times 0.10}{0.70\times 0.95+0.30\times 0.10}\\\\P(F\mid A)=\dfrac{0.03}{0.695}=0.043$

Hence, probability that students who did not attend the class on Fridays given that they passed the course is 0.043.

8 0

4 years ago

Who is faster? A girl who runs 200 meters in 28 seconds or her friend who runs 400 meters in 60 seconds? H.E.L.P

blagie [28]

Answer: The girl herself ran faster than her friend.

Step-by-step explanation:

This answer, of course assumes a lot of variables, but for the sake of keeping things simple, lets assume the following, the people are ran in a "straight line" with no "obstacles" in their way, and ran on the same track.

Calculating in meters-per-second for the girl who ran 200 meters in 28 seconds, you get 7.14285714286 meters per second

Calculating in meters-per-second for the girl who ran 400 meters in 60 seconds, you get 6.66666666667 meters per second

Comparing the two results, it can be "accurately" concluded that the girl herself ran faster than her friend under the following assumptions earlier stated.

4 0

4 years ago

Diego wants to find 4 1/5 - 7/10 .. Explain why he must rename 4 1/5 in order to do the subtraction?

nevsk [136]

Answer:

The result is 3 1/2 and this is the explanation why Diego must convert 4 1/5 from mixed number to improper fraction.

Step-by-step explanation:

These are the steps Diego should follow to find 4 1/5 - 7/10:

Step 1: Convert all mixed numbers into improper fractions.

4 1/5 = 21/5 - 7/10

Step 2: Find a common denominator between the improper fractions. When necessary, create equivalent fractions.

21/5 = 42/10 - 7/10

Step 3: Add or subtract the numerators and keep the denominator the same.

42 - 7 = 35/10

Step 4: If the answer is an improper form, reduce the fraction into a mixed number.

35/10 = 3 5/10 = 3 1/2

The result is 3 1/2 and this is the explanation why Diego must convert 4 1/5 from mixed number to improper fraction.

4 0

4 years ago