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3 years ago

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A humanities professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below th

e top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.

1 answer:

uysha [10]3 years ago

4 0

Answer:

Limits for B scores

( 79,2 ; 92 )

Step-by-step explanation:

The interval we are looking for is between 6 % and 59%

p₁ = 6 % p₁ = 0,06

As this point is at the right tail of the bell we better look for

p = 1- 0,06 p = 0,94

In z-table z score for 0,94062 is: z₁ = 1,56 ( 0,94062 ≈ 0,94 )

Doing the same to find z₂ score for 59% or 0,59

In z-table again

p = 0,59

z₂ = 0,023

Now we know

1,56 * σ = x₁ - 79

1,56*8,4 + 79 = x₁

x₁ = 92,10 or x₁ = 92

And

0,023*8,4 + 79 = x₂

x₂ = 79,19 or x₂ = 79,2

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Simplify using PEMDAS <br>2x - 3X + 4X -5X=

adoni [48]

Answer:

7

3x+4x=7x

2x_(_5x)

2x+5x=7x

7x+7x=14x

x=14÷2=7

4 0

3 years ago

You are at a stall at a fair where you have to throw a ball at a target. There are two versions of the game. In the first

Tomtit [17]

Answer:

$P(X=0)=(3C0)(0.1)^0 (1-0.1)^{3-0}=0.729$

And the probability of loss with the first wersion is 0.729

$P(Y=0)=(5C0)(0.05)^0 (1-0.05)^{5-0}=0.774$

And the probability of loss with the first wersion is 0.774

As we can see the best alternative is the first version since the probability of loss is lower than the probability of loss on version 2.

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

Alternative 1

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

$X \sim Binom(n=3, p=0.1)$

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:

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

We can find the probability of loss like this P(X=0) and if we find this probability we got this:

$P(X=0)=(3C0)(0.1)^0 (1-0.1)^{3-0}=0.729$

And the probability of loss with the first wersion is 0.729

Alternative 2

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

$Y \sim Binom(n=5, p=0.05)$

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

$P(Y)=(nCy)(p)^y (1-p)^{n-y}$

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

$nCy=\frac{n!}{(n-y)! y!}$

We can find the probability of loss like this P(Y=0) and if we find this probability we got this:

$P(Y=0)=(5C0)(0.05)^0 (1-0.05)^{5-0}=0.774$

And the probability of loss with the first wersion is 0.774

As we can see the best alternative is the first version since the probability of loss is lower than the probability of loss on version 2.

4 0

4 years ago

PLZZZ HELP IT'S FOR MIDDLE SCHOOLLLLL

Gre4nikov [31]

Answer:

B

Step-by-step explanation:

I think because if it weighs 25% more, then Jordans dog is the "1" part and Emmetts dog is the .25 part.

6 0

3 years ago

Read 2 more answers

Divide ratio <br><br> £360 in the ratio 1 : 8

lianna [129]

Answer --> 40 : 320

1/9 x 360 = 40
8/9 x 360 = 320

3 0

3 years ago

Find (f ∘ g)(-6) when f(x) = 9x + 2 and g(x) = -9x2 - 2x + 1.

Salsk061 [2.6K]

Given that the two functions are $f(x)=9x+2$ and $g(x)=-9x^2-2x+1$

We need to determine the value of $(f \circ g)(-6)$

<u>The value of </u> $(f \circ g)(x)$ <u>:</u>

The value of $(f \circ g)(x)$ can be determined using the formula,

$(f \circ g)(x)=f[g(x)]$

Substituting $g(x)=-9x^2-2x+1$ in the above formula, we get;

$(f \circ g)(x)=f[-9x^2-2x+1]$

Now, substituting $x=-9 x^{2}-2 x+1$ in the function $f(x)=9x+2$ , we get;

$(f \circ g)(x)=9(-9x^2-2x+1)+2$

$(f \circ g)(x)=-81x^2-18x+9+2$

$(f \circ g)(x)=-81x^2-18x+11$

Thus, the value of $(f \circ g)(x)$ is $(f \circ g)(x)=-81x^2-18x+11$

<u>The value of </u> $(f \circ g)(-6)$ <u>:</u>

The value of $(f \circ g)(-6)$ can be determined by substituting x = -6 in the function $(f \circ g)(x)=-81x^2-18x+11$

Thus, we have;

$(f \circ g)(-6)=-81(-6)^2-18(-6)+11$

$(f \circ g)(-6)=-81(36)-18(-6)+11$

$(f \circ g)(-6)=-2916+108+11$

$(f \circ g)(-6)=-2797$

Thus, the value of $(f \circ g)(-6)$ is -2797

Hence, Option B is the correct answer.

8 0

4 years ago