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3 years ago

What is the formula for 'percent of change'?

2 answers:

6 0

First: work out the difference (increase) between the two numbers you are comparing. Then: divide the increase by the original number and multiply the answer by 100. % increase = Increase ÷ Original Number × 100. If your answer is a negative number, then this is a percentage decrease. ( copy and paste from skillsyouneed.com )

Natasha_Volkova [10]3 years ago

6 0

Kenadiw is correct

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A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 stude

EleoNora [17]

Answer:

a) $P(X \leq 2)= P(X=0)+P(X=1)+P(X=2)$

And we can use the probability mass function and we got:

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

And adding we got:

$P(X \leq 2)=0.0115+0.0576+0.1369 = 0.2061$

b) $P(X=4)=(20C4)(0.2)^4 (1-0.2)^{20-4}=0.2182$

c) $P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]$

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

$P(X=3)=(20C3)(0.2)^3 (1-0.2)^{20-3}=0.2054$

And replacing we got:

$P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886$

d) $E(X) = 20*0.2= 4$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=20, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

We want this probability:

$P(X \leq 2)= P(X=0)+P(X=1)+P(X=2)$

And we can use the probability mass function and we got:

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

And adding we got:

$P(X \leq 2)=0.0115+0.0576+0.1369 = 0.2061$

Part b

We want this probability:

$P(X=4)$

And using the probability mass function we got:

$P(X=4)=(20C4)(0.2)^4 (1-0.2)^{20-4}=0.2182$

Part c

We want this probability:

$P(X>3)$

We can use the complement rule and we got:

$P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]$

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

$P(X=3)=(20C3)(0.2)^3 (1-0.2)^{20-3}=0.2054$

And replacing we got:

$P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886$

Part d

The expected value is given by:

$E(X) = np$

And replacing we got:

$E(X) = 20*0.2= 4$

3 0

3 years ago

Item 20 A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the sc

siniylev [52]

Answer:

The ratio of the area of the school banner to the area of the sign is <u>1944 cubic inches : 192.61 cubic inches.</u>

Step-by-step explanation:

Given:

A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches.

Now, to find the ratio of the area of the school banner to the area of the sign.

Dimensions of school banner :

Length = 54 inches.

Width = 36 inches.

Dimension of school sign:

Length = 17 inches.

So, to we find the width of sign by using cross multiplication method:

Let the width be $x.$

So, 54 is equivalent to 36.

Thus, 17 is equivalent to $x.$

$\frac{54}{36} =\frac{17}{x}$

By cross multiplying we get:

$54x=612$

Dividing both sides by 54 we get:

$x=11.33\ inches.$

Thus, the width of sign = 11.33 inches.

Now, to get the ratio of the area of the school banner to the area of the sign:

Area of the school banner : Area of the school sign.

= $54\times 36:17\times 11.33$

= $1944:192.61$

Therefore, the ratio of the area of the school banner to the area of the sign is 1944 cubic inches : 192.61 cubic inches.

6 0

3 years ago

Read 2 more answers

The average score on a standardized test is 750 points with a standard deviation of 50 points. What is the probability that a st

nalin [4]

The probability that student scored more than 850 we shall proceed as follows:
z=(x-μ)/σ
where:
x=850
μ=750
σ=50
thus
z=(850-750)/50
z=2
thus
P(x>850)=1-P(x<850)=1-P(z<2)=1-0.9772=0.0228

Answer: P(x>850)=0.0228

4 0

3 years ago

Read 2 more answers

A simple random sample of 13 four-cylinder cars is obtained, and the braking distances are measured. The mean braking distance i

Tanya [424]

G shshshusuj bshshsu. Haha yah

4 0

3 years ago

(3 x a−3/4)∙1/3 if a=3/8

Dennis_Churaev [7]

Answer:

1 3/8

Step-by-step explanation:

Possible derivation:

d/dx(1/8 (-2 + 3 x))

Factor out constants:

= 1/8 (d/dx(-2 + 3 x))

Differentiate the sum term by term and factor out constants:

= 1/8 d/dx(-2) + 3 d/dx(x)

The derivative of -2 is zero:

= 1/8 (3 (d/dx(x)) + 0)

Simplify the expression:

= 3/8 (d/dx(x))

The derivative of x is 1:

Answer: = 1 3/8

7 0

4 years ago

Read 2 more answers