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
What is the measure of angle x
Ugo [173]

Answer:

there is nothing to look at or answer

7 0
3 years ago
PLS HELP ASAP I DONT HAVE TIME AND IT ALSO DETECT IF ITS RIGHT OR WRONG!
IgorLugansk [536]
It’s C. Rational number
7 0
3 years ago
What technique does the author use most to describe Millicent?
Mkey [24]

The technique that the author used to describe Millicent in describing on how she looks would be direct characterization. Direct characterization is defined is a method used by most authors to describe the personality of a character. so your answer will be (d)


                                hope this helps:)

5 0
3 years ago
(x+y)(x+6y) pls help me solve question pls and pls also give explanation if possible
steposvetlana [31]

Step-by-step explanation:

= (x + y)(x + 6y)

= x \times x + x \times 6y + y \times x + y \times 6y

=  {x}^{2}  + 6xy + xy + 6 {y}^{2}

=  {x}^{2}  + 7xy + 6 {y}^{2}

7 0
2 years ago
A car rental agency charges 150 per week +0.45 per mile to rent car express the weekly cost to rent a car if as a function of th
Mashcka [7]

Answer:

The required function is:

C(x) = 150+0.45x

Step-by-step explanation:

We have to represent the given scenario as an equation or function

Let x be the number of miles driven in a week

Let C(x) be the function of the number of miles driven

As it is given that charges are 150 per week, these charges are constant so they will be used as it is.

It is also given that the cost of car is 0.45 per mile so for x miles the cost will be:

0.45x

Combining both terms, we get

C(x) = 150+0.45x

Hence,

The required function is:

C(x) = 150+0.45x

3 0
3 years ago
Other questions:
  • Olivia is growing roses and keeps track of how much fertilizer (in ounces) she adds to the soil and how many blooms each rose bu
    7·2 answers
  • Solve -1(4/5) please
    6·2 answers
  • A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsul
    11·1 answer
  • To begin solving this system of linear equations by elimination,you can add the equations
    5·1 answer
  • Solve for x using zeros of function method<br>-x³+2x²+x-2=0​
    10·1 answer
  • The volume of a sphere is 2304π in^3.<br><br>The radius of the sphere is ___ inches.​
    12·1 answer
  • Why did Keynes think deficit spending was necessary during periods of recession (such as the Great Depression)?
    5·1 answer
  • How does a translation move a figure?
    15·2 answers
  • Identify the ‘false’ statement.
    8·1 answer
  • 2.) If z varies inversely as r, and z= 24 when r = 6, find r when z= 12
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!