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
mojhsa [17]
3 years ago
14

Assume that SAT scores are normally distributed with mean 1518 and standard deviation 325. Round your answers to 4 decimal place

sa. If 100 SAT scores are randomly selected, find the probability that they have a mean less than 1500.b. If 64 SAT scores are randomly selected, find the probability that they have a mean greater than 1600c. If 25 SAT scores are randomly selected, find the probability that they have a mean between 1550 and 1575d. If 16 SAT scores are randomly selected, find the probability that they have a mean between 1440 and 1480.e. In part c and part d, why can the central limit theorem be used even though the sample size does not exceed 30?
Mathematics
1 answer:
Katyanochek1 [597]3 years ago
6 0

Answer:

a. 0.2898

b. 0.0218

c. 0.1210

d. 0.1515

e. This is because the population is normally distributed.

Step-by-step explanation:

Assume that SAT scores are normally distributed with mean 1518 and standard deviation 325. Round your answers to 4 decimal places

We are using the z score formula when random samples

This is given as:

z = (x-μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation.

n is the random number of samples

a.If 100 SAT scores are randomly selected, find the probability that they have a mean less than 1500.

For x = 1500, n = 100

z = 1500 - 1518/325/√100

z = -18/325/10

z = -18/32.5

z = -0.55385

Probability value from Z-Table:

P(x<1500) = 0.28984

Approximately = 0.2898

b. If 64 SAT scores are randomly selected, find the probability that they have a mean greater than 1600

For x = 1600, n = 64

= z = 1600 - 1518/325/√64.

z= 1600 - 1518 /325/8

z = 2.01846

Probability value from Z-Table:

P(x<1600) = 0.97823

P(x>1600) = 1 - P(x<1600) = 0.021772

Approximately = 0.0218

c. If 25 SAT scores are randomly selected, find the probability that they have a mean between 1550 and 1575

For x = 1550, n = 25

z = 1550 - 1518/325/√25

z = 1550 - 1518/325/5

z = 1550 - 1518/65

= 0.49231

Probability value from Z-Table:

P(x = 1550) = 0.68875

For x = 1575 , n = 25

z = 1575 - 1518/325/√25

z = 1575 - 1518/325/5

z = 1575 - 1518/65

z = 0.87692

Probability value from Z-Table:

P(x=1575) = 0.80974

The probability that they have a mean between 1550 and 1575

P(x = 1575) - P(x = 1550)

= 0.80974 - 0.68875

= 0.12099

Approximately = 0.1210

d. If 16 SAT scores are randomly selected, find the probability that they have a mean between 1440 and 1480

For x = 1440, n = 16

z = 1440 - 1518/325/√16

= -0.96

Probability value from Z-Table:

P(x = 1440) = 0.16853

For x = 1480, n = 16

z = 1480 - 1518/325/√16

=-0.46769

Probability value from Z-Table:

P(x = 1480) = 0.32

The probability that they have a mean between 1440 and 1480

P(x = 1480) - P(x = 1440)

= 0.32 - 0.16853

= 0.15147

Approximately = 0.1515

e. In part c and part d, why can the central limit theorem be used even though the sample size does not exceed 30?

The central theorem can be used even though the sample size does not exceed 30 because the population is normally distributed.

You might be interested in
Which equation describes the circle having center point (3,7) and the radius r=4 in Standard form
Annette [7]

The equation of circle in standard form is (x - 3)^2 + (y - 7)^2 = 16

<h3><u>Solution:</u></h3>

Given that circle having center point (3,7) and the radius r = 4

To find: equation of circle in standard form

<em><u>The equation of circle is given as:</u></em>

(x - h)^2 + (y - k)^2 = r^2

Where center (h,k) and radius r units

Given that center point (h , k) = (3, 7) and radius r = 4 units

Substituting the values in above equation of circle,

(x - 3)^2 + (y - 7)^2 = 4^2\\\\(x - 3)^2 + (y - 7)^2 = 16

Thus the equation of circle in standard form is (x - 3)^2 + (y - 7)^2 = 16

6 0
3 years ago
The chart below shows the average number of movies seen per person in selected countries. Use equal intervals to make a frequenc
NARA [144]
To make a frequency table, you will need to find the lowest and highest average number of movies.

Numbers go from 0.5 to 4.5.
And example of frequencies you could use are:

0-0.9 (1)
1-1.9(5)
2-2.9(5)
3-3.9(2)
4-4.9(1)

The frequencies are in parentheses beside the intervals.

6 0
3 years ago
When graphing a linear inequality, when can you NOT use (0, 0) as a test point to determine which side of a boundary line to sha
TEA [102]
When the point (0,0) is on the boundary line
8 0
3 years ago
Read 2 more answers
Jimmy’s family moved to a tropical climate. For the year that followed, he recorded the number of days that had a temperature ab
Phantasy [73]
The answer is 4) as it is more than 40 degrees
5 0
3 years ago
Help I cannot figure this question out.
netineya [11]

Answer:

B. x = -1 ± i

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Standard Form: ax² + bx + c = 0
  • Factoring
  • Quadratic Formula: \displaystyle x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

<u>Algebra II</u>

  • Imaginary Numbers: √-1 = i

Step-by-step explanation:

<u>Step 1: Define</u>

x² + 2x = -2

<u>Step 2: Identify Variables</u>

  1. Rewrite Quadratic in Standard Form [Addition Property of Equality]:        x² + 2x + 2 = 0
  2. Break up Quadratic:                                                                                        a = 1, b = 2, c = 2

<u>Step 3: Solve for </u><em><u>x</u></em>

  1. Substitute in variables [Quadratic Formula]:                                                \displaystyle x=\frac{-2 \pm \sqrt{2^2-4(1)(2)}}{2(1)}
  2. [√Radical] Evaluate exponents:                                                                     \displaystyle x=\frac{-2 \pm \sqrt{4-4(1)(2)}}{2(1)}
  3. Multiply:                                                                                                           \displaystyle x=\frac{-2 \pm \sqrt{4-8}}{2}
  4. [√Radical] Subtract:                                                                                        \displaystyle x=\frac{-2 \pm \sqrt{-4}}{2}
  5. [√Radical] Factor:                                                                                        \displaystyle x=\frac{-2 \pm \sqrt{-1}\sqrt{4}}{2}
  6. [√Radicals] Simplify:                                                                                       \displaystyle x=\frac{-2 \pm 2i}{2}
  7. Factor:                                                                                                             \displaystyle x=\frac{2(-1 \pm i)}{2}
  8. Divide:                                                                                                             \displaystyle x = -1 \pm i
3 0
3 years ago
Other questions:
  • Is this a function 2y+3x=6
    14·1 answer
  • Composite numbers have
    10·2 answers
  • Elena and her sister are sharing the cost of a digital camera. The camera costs $88.50. If Elena saved $50 to buy the camera, ho
    6·1 answer
  • Amanda’s hair grew 3/4 in. in 1 1/2 months? How long did her hair grow in one month?
    11·1 answer
  • How does interest rate affect money earned on a savings account?
    12·1 answer
  • SOLVE. 3 sin x + 5 cos x = 0
    13·2 answers
  • When given the lengths of the diagonals of a kite, which statement best explains how to find the area?
    13·2 answers
  • Previous balance: $1,221.35; payment: $300; new purchases: $25.90 and$18.53; periodic rate: 1.75%
    8·2 answers
  • 3. Given this quadratic equation, 2x2 - x - 28 = 0,
    5·1 answer
  • Martha has 124 bills consisting of 5-dollar bills and 10-dollar bills. If Martha has $840, how many of each kind of bill does sh
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!