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Nesterboy [21]
3 years ago
8

Your stats instructor graded your exams (0 to 100) and provided the exam summary statistics before returning the exam papers. Ex

ams scores were normally distributed with a mean of 70.5 and a standard deviation of 12.5. He assigns letter grades based on 100 points: 90 or higher is A; 80 < 90 is B; 70 < 80 is C; 60 < 70 is D; a
Mathematics
1 answer:
12345 [234]3 years ago
4 0

Answer:

The probability that a randomly selected student received a C or higher is 0.5160.

Step-by-step explanation:

Let <em>X</em> = scores received in an exam.

The random variable <em>X</em> follows a Normal distribution with parameters <em>μ</em> = 70.5 and <em>σ </em>= 12.5.

The stats instructor also graded the exams.

The grades were allotted as follows:

<u>Scores</u>    <u>Grades</u>

 > 90            A

90 - <80       B

80 - <70       C

70 - <60       D

  60 <           F

Compute the probability that a randomly selected student received a C or higher as follows:

P (C or higher) = P (X > 70)

                        =P(\frac{X-\mu}{\sigma}>\frac{70-70.5}{12.5})\\=P(Z>-0.04)\\=P(Z

*Use a <em>z-</em>table for the probability.

Thus, the probability that a randomly selected student received a C or higher is 0.5160.

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Answer: Hi!

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Rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$
solniwko [45]

Rewrite the expression  6j^2 - 4j + 12$ in the form $c(j + p)^2 + q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$

The ratio of \frac{q}{p}  = - 34

How to solve such questions?

Such Questions can be easily solved just by some Algebraic manipulations and simplifications. We just try to make our expression in the form which question asks us. This is the best method to solve such questions as it will definitely lead us to correct answers. One such method is completing the square method.

Completing the square is a method that is used for converting a quadratic expression of the form ax^{2} + bx + c to the vertex form

a(x - h)^{2} + k. The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: a(x + m)^{2} + n, such that the left side is a perfect square trinomial

$6j^2 - 4j +12$

=  $6(j^2 - \frac{2}{3} j )+12$

= $6(j^2 - \frac{2}{3} j  +  \frac{1}{9}  )+\frac{102}{9}                   (Completing Square method)

=6( j- \frac{1}{3} )^{2}  +  \frac{34}{3}

On comparing with the given equation we get

p = - \frac{1}{3}     and q = \frac{34}{3}

∴ \frac{q}{p} = \frac{\frac{34}{3} }{\frac{-1}{3} }

= - 34

Learn more about completing the square method here :

brainly.com/question/26107616

#SPJ4

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Jonathan records how 90 pupils travelled to school on one day and represents this information on the pie chart below.
xeze [42]

Answer:

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Step-by-step explanation:

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To solve this, you take f(x)-g(x) which is 2x^2-5-3x+3. This simplifies to 2x^2-3x-2.
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