3.16 SAT scores: SAT scores (out of 2400) are distributed normally with a mean of 1490 and a standard deviation of 295. Suppose a school council awards a certificate of excellence to all students who score at least 1900 on the SAT, and suppose we pick one of the recognized students at random. What is the probability this student's score will be at least 2100

Answers

Answer 1

Answer:

0.2333 = 23.33% probability this student's score will be at least 2100.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution, and conditional probability.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

SAT scores (out of 2400) are distributed normally with a mean of 1490 and a standard deviation of 295.

This means that [tex]\mu = 1490, \sigma = 295[/tex]

In this question:

Event A: Student was recognized.

Event B: Student scored at least 2100.

Probability of a student being recognized:

Probability of scoring at least 1900, which is 1 subtracted by the pvalue of Z when X = 1900. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1900 - 1490}{295}[/tex]

[tex]Z = 1.39[/tex]

[tex]Z = 1.39[/tex] has a pvalue of 0.9177

1 - 0.9177 = 0.0823

This means that [tex]P(A) = 0.0823[/tex]

Probability of a student being recognized and scoring at least 2100:

Intersection between at least 1900 and at least 2100 is at least 2100, so this is 1 subtracted by the pvalue of Z when X = 2100.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2100 - 1490}{295}[/tex]

[tex]Z = 2.07[/tex]

[tex]Z = 2.07[/tex] has a pvalue of 0.9808

This means that [tex]P(A \cap B) = 1 - 0.9808 = 0.0192[/tex]

What is the probability this student's score will be at least 2100?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0192}{0.0823} = 0.2333[/tex]

0.2333 = 23.33% probability this student's score will be at least 2100.


Related Questions

Solve For X (I could use some help because I'm confused on this)​

Answers

Answer:

X=10

Step-by-step explanation:

The arc is twice the angle, so 130.

12x+10=130

12x=130-10

12x=120

x=10

Dennis works at a frozen yogurt store in the summer. He
needs to order boxes of small cups and boxes of large cups.
The storage room can hold up to 10 more boxes of cups.
Each box of small cups costs $100 and each box of large
cups costs $150. A maximum of $1200 is budgeted for cups.
B. Graph The solutions of the system

Answers

Answer:

100x+150y≤1200

y≤8-2x/3

slope = -2/3

y-intercept = (0,8)

Step-by-step explanation:

I graphed it on my calculator but I'm not really sure how to explain it beyond just sharing a screenshot of the image

I hope that helps

A function is one to one if its graph passes the vertical line test. True or False???​

Answers

Answer:

False.

Step-by-step explanation:

please help me i really need help please

Answers

Answer:

45.18 mi

Step-by-step explanation:

What it is asking is to find the value of C.

Formula we're going to use:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

C is the hypotenuse.

Replace with given values, so

[tex] {19}^{2} + {41}^{2} = {c}^{2} [/tex]

Rewrite so there is no squared

[tex]361 + 1681 = {c}^{2} [/tex]

Add the numbers

[tex]2042 = {c}^{2} [/tex]

Find the value of C by square rooting 2042

[tex] \sqrt{2042} = 45.1884941108[/tex]

Answer:

[tex]45.18 \: mi[/tex]

^ 45.19 mi if teacher wants you to round

What is the answer I need to know

Answers

Answer:

Arrange your numbers in numerical order.

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

Find the volume of the triangular prism below.

A) 28 cubic feet

B) 168 cubic feet

C) 84 cubic feet

D) 52.5 cubic feet

Answers

Answer:

b.168

Step-by-step explanation:

find the probability that a randomly selected point within the circle falls in the red shaded area round to the nearest hundredth r = 4 cm 2.5 cm 3 cm 3 cm

Answers

Answer:

[tex]p\approx 0.39[/tex]

Step-by-step explanation:

We are given a circle of radius 4 cm, and a triangle inscribed within the circle with a vertical height of 6.5 cm and a base of 6 cm.

To find the probability a randomly selected point lands in the red area, we can divide the red area by the total area.

The area for a circle is given by:

[tex]A=\pi r^2[/tex]

Since the radius is 4 cm, the area of the circle or total area is:

[tex]A=\pi (4)^2=16\pi \text{ cm}^2[/tex]

The area for a triangle is given by:

[tex]\displaystyle A=\frac{1}{2}bh[/tex]

The base of the triangle is 6 cm total and the vertical height is 6.5 cm. Therefore, the area is:

[tex]\displaystyle A=\frac{1}{2}(6)(6.5)=19.5\text{ cm}^2[/tex]

The probability of landing in the red shaded area is:

[tex]\displaystyle p=\frac{\text{Red Region}}{\text{Total Region}}[/tex]

Therefore:

[tex]\displaystyle p=\frac{19.5}{16\pi}\approx 0.39=39\%[/tex]

PLS HELP HELP ME WITH a question pls ​

Answers

Step-by-step explanation:

d.

e +e+25=180°{sum of angle of triangle}

2e+25=180°

2e=155

e=155/2

e=77.5°

e.

55°+55°+f=180°{sum of angle of triangle}

f=180-110

f=70°

hope it helps.

PLEASE HELP IM GIVING 100 POINTS AND BRAINLIEST IF THE ANSWERS RIGHT
A six-sided number cube labeled 1 through 6 is rolled 600 times. An odd number is rolled 272 times. Compare the experimental probability of rolling an odd number with the relative frequency of rolling an odd number and select one of the statements below that best describes the situation. (5 points)

a
The experimental probability and relative frequency are the same.

b
The experimental probability is larger than the relative frequency.

c
The experiment probability is smaller than the relative frequency.

d
There is not enough information to determine the relative frequency.

Answers

Answer:

Relative frequency is defined as the number of "desired" results divided by the total number of possible results. Experimental probability is defined the same way. This means that the first choice is best, the experimental probability and relative frequency are the same.

The theoretical probability, on the other hand, would be 0.5, or 300/600, which is larger than the experimental probability.

Step-by-step explanation:

btw im in middle school

True or False.

The expressions 3+y and 13(6+y) are equivalent?



True

False

Answers

Answer:

False

Step-by-step explanation:

Brainliest please?

Help fast please....

Answers

Answer:

46 yd²

Step-by-step explanation:

A rectangular prism has a volume of 240cm. It's height measures 8 cm. What is the area of its base

Answers

Answer: Base = 90 [tex]cm^{2}[/tex]

Step-by-step explanation:

7m - 13 = 43 plzzzzzzzzzzzz help

Answers

M=8 im not sure if this answers your question

Answer:

=8

Step-by-step explanation:

7m-13=43

7m-13+13=43+13

7m=8

What is the area of the shaded region?

Answers

Area of a rectangle = length * width
So in this since, the area of the shaded area (which Is the whole rectangle)
A = 200ft * 100ft
A = 20,000

Answer:

17,680 ft²

Step-by-step explanation:

Shaded area = entire shaded rectangle area - unshaded rectangle area - square area

A = 200(100) - 24(30) - 40²

A = 20,000 - 720 - 1600 = 17,680

Como cálculo el área de las figuras geometrícas porfa para una persona de 5to ​

Answers

Answer:

Se calcula sumando todos los lados (siempre y cuando tengan las mismas unidades). El área de una figura de dos dimensiones se calcula contando el número de cuadrados que pueden cubrir la figura.

Step-by-step explanation:

look at the picture. please please help im stuck.​

Answers

Answer:

7 is greater than or equal to x.

Answer:

Hey I’m not sure but I think it’s A

Step-by-step explanation:

In the expression “six to the power
of four is 1,296," which number is the
base?

Answers

Six is the base because 6^4 is 1296.

PLS HELP
Simply the expression by combining like terms.
6x+9+2x+4=

Answers

Answer:

Combine like terms: 18x + 15x = 33x

(45 + 33x + 6x2)

Step-by-step explanation:

Answer:

Combine like terms: 18x + 15x = 33x

(45 + 33x + 6x2)

Step-by-step explanation:

A bowl of cold gazpacho soup is warming to room temperature. The temperature difference
between the soup and the room decreases by 5% every minute. What will the temperature
difference be in 8 minutes if it is currently 24°C?
If necessary, round your answer to the nearest tenth.

Answers

Answer: 25

Step-by-step explanation:

I need help with this !!!

Answers

Answer:

no it cannot be

Step-by-step explanation:

because :

2/10 equals to 10/2 So 6/10 ÷ 2/10 =6/10×10/2

6×10=60

10×2=20 after reducing the fraction its 3/1

3 Convert 6,23 kg to grams​

Answers

Answer:

6230 grams xD

Step-by-step explanation:

6230 grams..

( it says i have to write 20 letters so i just did this)

PLSSS HELP DUE IN 5 MINUTES!!!!
PLEASE DO NOT ANSWER JUST FOR POINTS!!!

LOOK AT THE IMAGE FOR THE QUESTIONS AND ANSWERS
NOTE: The first answer “(0,9)” is incorrect I tried and it was wrong so please it’s either (9,0) or (3,0)

Answers

Answer:

I think it's (0,3) sorry if it not

Answer:

(3, 0)

Step-by-step explanation:

The vertex point is 3 units to the right of the origin, making the x-coordinate 3, but it doesn’t move up or down, meaning that the y-coordinate is 0.

so it’s (3,0)

Btw, the vertex is the point of the parabola where it’s the minimum or maximu (minimum in this case). You answered for the y-interceptm which is where the parabola touches the y-axis.

divide 5/8 3/4 in the most simple form

Answers

Answer:

15/32

3/4 x 5/8 = 15/32 in fraction form.

Step-by-step explanation:

What is the equation that represents the relationship shown in the table?​

Answers

The equation is x+8=y

what expression is equivalent to 2(x-4)+x

Answers

Step-by-step explanation:

2(x-4) + x

= 2x-8 + x

= 3x - 7

The perimeter of a worksheet is 40 inches. It is 13 inches long . How tall is it?

Answers

Answer:

TALA RHYTHMIC PATTERNS

ACTIVITY 2: LET'S DO TALA

kind of membranophones/percussion instruments found at home for tapping. Record your

Directions: Perform the following tala rhythmic patterns using the given legend. Use any

performance using any recorder and send it to your

INSTRUMENTS AT HOME

MANJIRA

TIN CANS

1 2 3 4 5 6

х

1 2 3 4 5 6 7 8 9 10 11 12

GHATAM

PAL

X

х

0 X

TABLA

1 2 3 4 5 6 7 8 9 10

BOX

x xox

HELP ASAP PLZ DONT GUESS THIS DEPENDS ON MY LIFE FRR(graph in pic)

If Sheila rotates triangle PQR 90° counterclockwise to form triangle LMN, what is the measure of angle MNL?
A.130 °
B.100 °
C.50 °
D.30 °

Answers

Answer:

30

Step-by-step explanation:

This is a bit nasty, but you must keep the order in mind. PQR means that Q is the middle letter. M is also the middle letter. That's the easy part. What does MNL mean?

The lettering goes clockwise. MNL is the same thing as QRP. So what is R?

50 + 100 + R = 180

150 + R = 180

R = 180 - 150

R = 30

Calculator
Enter the unknown value that makes this statement true:
25% of O
is 30.
->
-
1
2
3

Answers

Answer:

X = 120

Step-by-step explanation:

here's your solution

=> we need to find the number whose 25%

is 30

=>. now , let the number be X

=> solve for X

=>. 25/100*X = 30

=> X = 30*100/25

=> X = 120

hope it helps

somebody please help me with math ;-;:

what is the equation for this table?

X 2 4 5 8 12
Y 11 13 14 17 21

options:

1.y = x + 9
2.y = x - 9
3.y = x ÷ 9
4.y = 9 x

Answers

Answer:

y=x+9

Step-by-step explanation:

2+9=11,4+9=13,5+9=14,9+8=17,12+9=21

hey guys i need some help on this division problem i have

Answers

Answer:

3. 25/28

4. 1 1/7

Step-by-step explanation:

when you divide fractions just flip one of them and then multiply across

so instead of 5/7 ÷ 4/5 its

5/7 • 5/4

please mark me brainliest to help me get ace rank

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