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
Burka [1]
3 years ago
6

The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probab

ility that the sample mean will be larger than 1224? b) What is the probability that the sample mean will be less than 1230? c) What is the probability that the sample mean will be between 1200 and 1214? d) What is the probability that the sample mean will be greater than 1200? e) What is the probability that the sample mean will be larger than 73.46?
Mathematics
1 answer:
LiRa [457]3 years ago
5 0

Answer:

a) 0.0082

b) 0.9987

c) 0.9192

d) 0.5000

e) 1

Step-by-step explanation:

The question is concerned with the mean of a sample.  

From the central limit theorem we have the formula:

z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }

a) z=\frac{1224-1200}{\frac{60}{\sqrt{36} } }=2.40

The area to the left of z=2.40 is 0.9918

The area to the right of z=2.40 is 1-0.9918=0.0082

\therefore P(\bar X\:>\:1224)=0.0082

b) z=\frac{1230-1200}{\frac{60}{\sqrt{36} } }=3.00

The area to the left of z=3.00 is 0.9987

\therefore P(\bar X\:

c) The z-value of 1200 is 0

The area to the left of 0 is 0.5

z=\frac{1214-1200}{\frac{60}{\sqrt{36} } }=1.40

The area to the left of z=1.40 is 0.9192

The probability that the sample mean is between 1200 and 1214 is

P(1200\:

d) From c) the probability that the sample mean will be greater than 1200 is 1-0.5000=0.5000

e) z=\frac{73.46-1200}{\frac{60}{\sqrt{36} } }=-112.65

The area to the left of z=-112.65 is 0.

The area to the right of z=-112.65 is 1-0=1

You might be interested in
I need to find out x Q = 2x + 3 = 7
AlekseyPX
After subtracting 3 from 7, and dividing 4 by 2, you should end up with x=2.
3 0
3 years ago
Identify the common external tangent.<br><br> line r<br> line s<br> segment AB
Oxana [17]
The external tangent is line s
8 0
3 years ago
Read 2 more answers
(15.2*0.25-48.51/14.7)/x=(13/44-2/11-5/66/2.50)1.2/(3.2+0.8(5.5-3.25)
goldfiish [28.3K]

Answer:

x = 41.67

Step-by-step explanation:

The above equation, would be simplified or divided into parts;

Therefore, the given equation becomes;

A/x = B/C

Where;

A = (15.2*0.25-48.51/14.7)

B = (13/44-2/11-5/66/2.50)1.2

C = 3.2+0.8(5.5-3.25)

x = unknown variable.

<u>Part A</u>

(15.2*0.25-48.51/14.7) = (15.2*0.25 - 3.3)

A = (3.8 - 3.3)

A = 0.5

<u>Part B</u>

(13/44-2/11-5/66/2.50)1.2 = (0.3 - 0.18 - 0.030) * 1.2

B = 0.09 * 1.2

B = 0.108

<u>Part C</u>

(3.2+0.8(5.5-3.25)

C = 4*(2.25)

C = 9

<em>Substituting the values into the equation, we have;</em>

0.5/x = 0.108/9

<em>Cross-multiplying, we have;</em>

9 * 0.5 = 0.108x

4.5 = 0.108x

x = 4.5/0.108

x = 41.67

6 0
2 years ago
A bag contains 15 red candies, 15 yellow candies, and 15 blue candies. What is the probability of randomly
masya89 [10]

|\Omega|=45\cdot44=1980\\|A|=15\cdot14\cdot3=630\\\\P(A)=\dfrac{630}{1980}=\dfrac{7}{22}\approx31.8\%

6 0
2 years ago
A large home improvement store is considering expanding its selection of moving products, such as cardboard boxes and packing ta
fiasKO [112]

Answer:

The store can be 90% confident that the interval from 0.293 to 0.355 captures the proportion of all customers of this store who have moved in the past 5 years.

Step-by-step explanation:

The confidence interval provides a range of values (lower and upper bound) based on a certain confidence level at which the true proportion or mean value of a given sample mean or proportion exists. In the scenario above, the confidence level is 90% and the confidence interval is 0.293 to 0.355. Hence, we can be 90% confident that the true proportion of all customers of the store who have moved within the last five years exists within this interval.

8 0
3 years ago
Other questions:
  • Ed is 7 years older than Ted. Ed’s age is also 3/4 times Ted’s age. How old are Ed and Ted?
    9·1 answer
  • OFFERING 10 POINTS
    11·1 answer
  • "According to contractarian logic, we should be willing to make concessions to others if they agree to make comparable and recip
    5·1 answer
  • Each of the 12 cards shown has a number and a color or pattern. Each card is equally likely to be drawn. Find each probability.
    12·1 answer
  • Write f(x)=8x^2-4x+11 in vertex form
    10·1 answer
  • Find <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D" id="TexFormula1" title="\frac{dy}{dx}" alt="\frac{dy}{dx}" align
    6·2 answers
  • Question 3 A study was performed to determine whether men and women differ in their repeatability in assembling components on pr
    15·1 answer
  • Look at this cube:
    13·1 answer
  • How many combinations of powerball numbers are there
    11·2 answers
  • Help help help plz pretty plz
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!