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
Volgvan
3 years ago
11

The average THC content of marijuana sold on the street is 9.3%. Suppose the THC content is normally distributed with standard d

eviation of 1%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible, a. What is the distribution of X? X ~ N( 9.3 Correct, 1 Correct) b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 9.2. 0.4601 Incorrect c. Find the 75th percentile for this distribution. 8
Mathematics
1 answer:
velikii [3]3 years ago
8 0

Answer:

a) X \sim N(9.3,1)  

b) P(X>9.2)=P(\frac{X-\mu}{\sigma}>\frac{9.2-\mu}{\sigma})=P(Z>\frac{9.2-9.3}{1})=1-P(Z

c) The value of height that separates the bottom 75% of data from the top 25% is 9.9745.  

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(9.3,1)  

Where \mu=9.3 and \sigma=1

3) Part b

We are interested on this probability

P(X>9.2)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>9.2)=P(\frac{X-\mu}{\sigma}>\frac{9.2-\mu}{\sigma})=P(Z>\frac{9.2-9.3}{1})=1-P(Z

4) Part c

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.6745. On this case P(Z<0.6745)=0.75 and P(z>0.6745)=0.25

If we use condition (b) from previous we have this:

P(X  

P(Z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.6745

And if we solve for a we got

a=9.3 +1*0.6745=9.9745

So the value of height that separates the bottom 75% of data from the top 25% is 9.9745.  

You might be interested in
Factorize (2u+3u)(u+v)-2u+3v​
Stolb23 [73]

Answer:

Step-by-step explanation:

(2u+3u)(u+v)-2u+3v

=2u(u+v)+3u(u+v)-2u+3v

=2u^2+2uv+3u^2+3uv-2u+3v

=5u^2+5uv-2u+3v

7 0
2 years ago
Given that (ax^2 + bx + 3) (x + d) = x^3 + 6x^2 + 11x + 12<br> a + 2b - d = ?
Mariulka [41]

Answer:

Let's solve for a.

(ax2+bx+3)(x+d)=x3+6x2+11x+12a+2b−d

Step 1: Add -12a to both sides.

adx2+ax3+bdx+bx2+3d+3x+−12a=x3+6x2+12a+2b−d+11x+−12a

adx2+ax3+bdx+bx2−12a+3d+3x=x3+6x2+2b−d+11x

Step 2: Add -bdx to both sides.

adx2+ax3+bdx+bx2−12a+3d+3x+−bdx=x3+6x2+2b−d+11x+−bdx

adx2+ax3+bx2−12a+3d+3x=−bdx+x3+6x2+2b−d+11x

Step 3: Add -bx^2 to both sides.

adx2+ax3+bx2−12a+3d+3x+−bx2=−bdx+x3+6x2+2b−d+11x+−bx2

adx2+ax3−12a+3d+3x=−bdx−bx2+x3+6x2+2b−d+11x

Step 4: Add -3d to both sides.

adx2+ax3−12a+3d+3x+−3d=−bdx−bx2+x3+6x2+2b−d+11x+−3d

adx2+ax3−12a+3x=−bdx−bx2+x3+6x2+2b−4d+11x

Step 5: Add -3x to both sides.

adx2+ax3−12a+3x+−3x=−bdx−bx2+x3+6x2+2b−4d+11x+−3x

adx2+ax3−12a=−bdx−bx2+x3+6x2+2b−4d+8x

Step 6: Factor out variable a.

a(dx2+x3−12)=−bdx−bx2+x3+6x2+2b−4d+8x

Step 7: Divide both sides by dx^2+x^3-12.

a(dx2+x3−12)

dx2+x3−12

=

−bdx−bx2+x3+6x2+2b−4d+8x

dx2+x3−12

a=

−bdx−bx2+x3+6x2+2b−4d+8x

dx2+x3−12

Answer:

a=

−bdx−bx2+x3+6x2+2b−4d+8x/

dx2+x3−12

Step-by-step explanation:

8 0
3 years ago
Kerry's saving account has balance of $372 for grandmother is going to give her a birthday check was 1/4 of her savings parents
igor_vitrenko [27]

Answer:

Step-by-step explanation:

372 + 1/4*372 = $465

$465 is her new savings and 33% of it is $153.45

$465 + $153.45 = $618.45

So yes she would have enough money to buy a plane ticket to alaska the cost $600

6 0
2 years ago
Michael made 9/12 of his free throws at practice. What is 9/12 in simplest form?
riadik2000 [5.3K]
It would be 0.75 as a decimal or 3/4
4 0
3 years ago
Read 2 more answers
Draw a picture of 3 5/7 as a fraction.
natima [27]

If you would do this in whole number form, it'll be 40/7.

3 0
2 years ago
Read 2 more answers
Other questions:
  • What is x if the equation is, 4 - (2x-3) = 3?
    7·1 answer
  • 25 POINTS HELP NOW<br><br> Twenty is 10% of what number?<br><br> Enter your answer in the box
    7·2 answers
  • 1. write an equation in point slope form that passes through the point (2,3) and slope of -4
    7·1 answer
  • Set up a proportion table. for: At a hardware store, the price of 3 feet of rope is $1.20. What is the price of 8 feet of rope?
    8·2 answers
  • Simply: 2 (x+8)+6x<br> Thanks
    8·1 answer
  • PLEASE HELP ASAP 45 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
    5·1 answer
  • 11 and 12 and the work plsss
    10·1 answer
  • Which function is graphed?<br>​
    15·1 answer
  • find the greatest possible length which can be used to measure exactly the lengths 4m 95cm; 9m and 16m 65cm?​
    13·1 answer
  • Please help me solve this in exponents form ive been having troubles on mynmath homework (3x^6 y^2)^3 × 2x^10 y^-7
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!