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
Genrish500 [490]
2 years ago
7

The prices of all college textbooks follow a bell-shaped distribution with a mean of $113 and a standard deviation of $12. Using

the empirical rule, find the interval that contains the prices of 99.7% of college textbooks.
Mathematics
1 answer:
Soloha48 [4]2 years ago
5 0

Step-by-step explanation:

In statistics, the empirical rule states that for a normally distributed random variable,

  • 68.27% of the data lies within one standard deviation of the mean.

  • 95.45% of the data lies within two standard deviations of the mean.

  • 99.73% of the data lies within three standard deviations of the mean.

In mathematical notation, as shown in the figure below (for a standard normal distribution), the empirical rule is described as

                             \Phi(\mu \ - \ \sigma \ \leq X \ \leq \mu \ + \ \sigma) \ = \ 0.6827 \qquad (4 \ \text{s.f.}) \\ \\ \\ \Phi(\mu \ - \ 2\sigma \ \leq X \ \leq \mu \ + \ 2\sigma) \ = \ 0.9545 \qquad (4 \ \text{s.f.}) \\ \\ \\ \Phi}(\mu \ - \ 3\sigma \ \leq X \ \leq \mu \ + \ 3\sigma) \ = \ 0.9973 \qquad (4 \ \text{s.f.})

where the symbol \Phi (the uppercase greek alphabet phi) is the cumulative density function of the normal distribution, \mu is the mean and \sigma is the standard deviation of the normal distribution defined as N(\mu, \ \sigma).

According to the empirical rule stated above, the interval that contains the prices of 99.7% of college textbooks for a normal distribution N(113, \ 12),

                \Phi(113 \ - \ 3 \ \times \ 12 \ \leq \ X \ \leq \ 113 \ + \ 3 \ \times \ 12) \ = \ 0.9973 \\ \\ \\ \-\hspace{1.75cm} \Phi(113 \ - \ 36 \ \leq \ X \ \leq \ 113 \ + \ 36) \ = \ 0.9973 \\ \\ \\ \-\hspace{3.95cm} \Phi(77 \ \leq \ X \ \leq \ 149) \ = \ 0.9973

Therefore, the price of 99.7% of college textbooks falls inclusively between $77 and $149.

You might be interested in
Help with these plz thanks
asambeis [7]

10x = 5 Answer: x = 1/2

−5 = x + 6 Answer: x = -11

22 = 22x Answer: x = 1

0 = −7x Answer: x = 0

−x = 7 Answer: x = -7

x/4 = 1/2 Answer: x = 2

x/5 = 20 Answer: x = 100

x/-2 = -5 Answer: x = 10

5x = 55 Answer: x = 11

−3x = 18 Answer: x = -6

12 = x -6 Answer: x = 18

7 0
3 years ago
WILL MARK AS BRAINLIEST PLZ HELP
nignag [31]
The formula is
I=prt
I interest earned 14.65
P initial deposit ?
R interest rate 0.025
T time 2 years
Plug in the formula
14.65=p×0.025×2
Solve for p
14.65=0.05p
Divide both sides by 0.05
P=14.65/0.05
P=293....answer

Hope it helps!
7 0
3 years ago
Read 2 more answers
I will give brainliest if this is answerd in 10 min it is timed here it is:this is worth 100 pts
Jobisdone [24]

Answer:

customary system:

miles

ounces

metric system:

deciliters

kilometers

centigram

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
John needs to put tape around 40 windows in a building before the painters can get to work. Each window measures 3 feet by 4 fee
tangare [24]
600 feet of tape because 4 +4 for two sides of the window is 8 and 3+ 3 is 6, 14 plus the foot of overlap is 15 x 40 is 600.
3 0
3 years ago
If (X + 8) is a factor of f(x), which of the following must be true?
julsineya [31]

Answer: C

Step-by-step explanation:

If (X + 8) is a factor of f(x), then to find the root, equate the factor to zero. That is,

X + 8 = 0

X = 0 - 8

X = -8

If -8 is substituted into f(x), the equation will tend to zero. That is,

F( -8 ) = 0

C is therefore the correct answer.

4 0
3 years ago
Other questions:
  • PLEASE HELP ME I BEG YOU
    6·1 answer
  • Which of the following is equivalent to (2x + 4xy + 5y) – (x + 3y)?
    14·2 answers
  • Three randomly chosen people decide to check the calendar from the year they were born to see what day of the week they were bor
    15·1 answer
  • 0=4t-16t^2 Solve this please
    12·1 answer
  • A set of bivariate data was used to create a least squares regression line. Which of the following is minimized by the line
    12·2 answers
  • I need help I don't understand this
    12·2 answers
  • If a windmill with radius 26 feet makes 12 full revolutions every 1 minute, what is its linear speed?
    15·1 answer
  • In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=52°, and JH = 4.2 feet. Find the length of IJ to the nearest tenth of a foot.
    5·1 answer
  • QUESTION WORTH 15 POINTS!! FINALS!! NO WRONG ANSWERS PLEASE!!
    14·1 answer
  • Liz decides to save money to buy an electric car. She invests $500 every 6 months at
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!