1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Juli2301 [7.4K]
3 years ago
8

The national average for the math portion of the College Board’s Scholastic Aptitude Test

Mathematics
1 answer:
Alex73 [517]3 years ago
4 0

Answer:

a) 0.1587

b) 0.023

c) 0.341

d) 0.818

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 515

Standard Deviation, σ = 100

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(score greater than 615)

P(x > 615)

P( x > 615) = P( z > \displaystyle\frac{615 - 515}{100}) = P(z > 1)

= 1 - P(z \leq 1)

Calculation the value from standard normal z table, we have,  

P(x > 615) = 1 - 0.8413 = 0.1587 = 15.87\%

b) b) P(score greater than 715)

P(x > 715) = P(z > \displaystyle\frac{715-515}{100}) = P(z > 2)\\\\P( z > 2) = 1 - P(z \leq 2)

Calculating the value from the standard normal table we have,

1 - 0.977 = 0.023 = 2.3\%\\P( x > 715) = 2.3\%

c) P(score between 415 and 515)

P(415 \leq x \leq 515) = P(\displaystyle\frac{415 - 515}{100} \leq z \leq \displaystyle\frac{515-515}{100}) = P(-1 \leq z \leq 0)\\\\= P(z \leq 0) - P(z < -1)\\= 0.500 - 0.159 = 0.341 = 34.1\%

P(415 \leq x \leq 515) = 34.1\%

d) P(score between 315 and 615)

P(315 \leq x \leq 615) = P(\displaystyle\frac{315 - 515}{100} \leq z \leq \displaystyle\frac{615-515}{100}) = P(-2 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -2)\\= 0.841 - 0.023 = 0.818 = 81.8\%

P(315 \leq x \leq 615) = 81.8\%

You might be interested in
Please help me i need an answer
prohojiy [21]
Let the number be n
Part A- 2/3  + n = 2n+3
Part B- n= 2/3 -3
 n= 2-9 / 3
n= -7/3 =-2.33
3 0
3 years ago
Read 2 more answers
What is the simplified form of the expression? (m^-1m^5/m^-2)^-3
Eva8 [605]
1 (((m^(-1)) (m^5)) / (m^(-2)))^(-3) =1/m^18
5 0
3 years ago
Read 2 more answers
Which are not the dimensions
Paul [167]
It would be B. 5cm 12cm and 13cm
4 0
2 years ago
Help me out plzzz???!
nlexa [21]

Answer:

1/4x^2 - 1/4x - 1/4

Step-by-step explanation:

I multiplied the two binomials at the top to get 6x^2 + x -2 and I divided it by 24x^2 - 4x - 8 and simplified it to get 1/4x^2 - 1/4x - 1/4

4 0
3 years ago
Due to be heavy rain , Mother warned Dia not to go in
ehidna [41]

Answer:

Hi,

6

Step-by-step explanation:

the number divided by 5 has a remainder of 1 , its last digit is 1 or 6.

the number is divisible by 2, its last digit is 0 or 2,or 4, or 6 or 8.

Both conditions give : the last digit must be 6.

8 0
3 years ago
Other questions:
  • Sheila started the geometric pattern shown below. 1 , 3 , 9 , 27 If the pattern continues as shown , what is the next term in th
    14·2 answers
  • A change in the dollar price of yen from $1 = 100 yen to $1 = 50 yen will:
    5·1 answer
  • So far, we have only focused on estimating the mean living area in homes in Ames. # Now you'll try to estimate the mean home pri
    15·1 answer
  • The floor of a rectangular cage has a length 4 feet greater than its width, w. James
    15·1 answer
  • What is the leading coefficient of the polynomial f(c) defined below? need help asap!
    5·1 answer
  • Decrease 20g by 90% I don’t get this
    9·2 answers
  • A store sells a package of 25 trading cards for $5.25. Explain how you can tell that the unit price is less that $1. What is the
    6·1 answer
  • David rents DVDS from a company that changes a $7.00 monthly fee and $1.50 for each dvd rental. He ends up paying $20.50 for the
    5·1 answer
  • Hello! Any help is appreciated (:
    8·2 answers
  • How many characteristics of a population does a random variable represent?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!