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2 years ago

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The average score of students in Mr. Blake's science class was 73 with a standard deviation of 11, while the average score of st

udents in Mrs. Arnold's class was 75 with a standard deviation of 10. Which class is more variable?

1 answer:

Pani-rosa [81]2 years ago

3 0

Answer:

Mr Blake's science class

Step-by-step explanation:

The standard deviation is a measure of variation.

It tells us how far each of the data set in the distribution are far from the mean of the distribution.

The average score of students in Mr. Blake's science class was 73 with a standard deviation of 11, while the average score of students in Mrs. Arnold's class was 75 with a standard deviation of 10.

Since 11>10, Mr Blake's science class is more variable than Mrs. Arnold's class.

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Answer:

Slope of the function is $=3.75$ ,Y-intercept $=20$ .

The function is $y=3.75(x)+20$ with initial value $=20$ ,Jordan puts $\$3.75$ each week andthe amount saved by Jordan after $52$ week $=215\$$ .

Step-by-step explanation:

To understand the slope and y-intercept lets assign $x$ as number of weeks and $y$ as the money saved by Jordan.

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SImilarly

We have $(x,y) =(0,20)$ and $(x_1,y_1) =(25,113.75)$

Part A:

The function is $y=m(x)+b$

From point-slope form,we have slope (m)

and $m=\frac{y_1-y}{x_1-x}$ ,plugging the values of the points.

$m=\frac{113.75-20}{25-0}=3.75$

Y-intercept of this function is the constant term or the money of $\$20$ that is already inside the money bank.

We can also calculate y-intercept by arranging the function as $b=y-m(x)$ choosing any $(x_1,y_1) = (25,113.75)$ coordinate and here $b$ is the y-intercept.

The result will be same.

Part B:

The equation <u> $y=3.75(x)$ </u> can represent the function described.

And the initial value is the <u>y-intercept $=\$20$ </u>

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After $52$ week the amount saved by Jordan ,here $x=52$ ,as the x-variable is the number of weeks.

Plugging the value of $x=52$ in $y=m(x)+b$ where $m=3.75$ so the equation becomes $y=3.75(x)+20$

$y=3.75(x)+20 =3.75(52)+20=\$215$

So basically the function is $y=3.75(x)+20$ and the amount saved by Jordan after $52$ week $=215\$$ .

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Answer:

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$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

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c) $Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

d) $P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

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".

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

$X \sim Binom(n=4, p=1-0.25=0.75)$

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

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

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3 years ago