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
Ierofanga [76]
3 years ago
7

Delicious Candy markets a two-pound box of assorted chocolates. Because of imperfections in the candy making equipment, the actu

al weight of the chocolate has a uniform distribution ranging from 31.8 to 32.6 ounces. a. Define a probability density function for the weight of the box of chocolate. b. What is the probability that a box weighs (1) exactly 32 ounces; (2) more than 32.3 ounces; (3) less than 31.8 ounces? c. The government requires that at least 60% of all products sold weigh at least as much as stated weight. Does Delicious Candy violate government regulation?
Mathematics
1 answer:
nikitadnepr [17]3 years ago
8 0

Answer:

a. f(x)= 1.25\ \ \ \ , \  for \ 31.8\leq x\leq 32.6

b. \ P(X=32)=0\\P(X>32.3)=0.375\\P(X

c. No.  Delicious Candy isn't violating any government regulations

Step-by-step explanation:

a.

-A uniform distribution is given by the formula:

f(x)=\frac{1}{b-a} \ \ \ for \ \ \ a\leq x\leq b

#we substitute our values in the formula above to determine the distribution:

f(x)=\frac{1}{b-a}\\\\=\frac{1}{32.6-31.8}\\\\=1.25\\\\\therefore f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6

Hence, the probability density function for the box's weight is given as: f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6

b. The probability of the box's weight being exactly 32 ounces is obtained by integrating f(x) over a=b=32:

f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32}_{32} {1.25} \, dx \\\\\\=[1.25x]\limits^{32}_{32}\\\\\\=1.25[32.0-32.0]\\\\\\=0

Hence,  the probability that a box weighs exactly 32 ounces is 0.000

ii.The probability that a box weighs more than 32.3 is obtained by integrating f(x) over the limits 32.3 to 32.6 :

f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32.6}_{32.3} {1.25} \, dx \\\\\\=[1.25x]\limits^{32.6}_{32.3}\\\\\\=1.25[32.6-32.3]\\\\\\=0.375

Hence, the probability that a box weighs more than 32.3 ounces is 0.3750

iii. The probability that a box weighs less than 31.8 is 0.000 since the weight limits are 31.8\leq x\leq 32.6.

-Any value above or below these limits have a probability of 0.000

c. Let 32 ounces be the government's stated weight.

1.25(32.6-32)=0.75\\\\0.75>0.60

Hence, Delicious Candy isn't violating any government's regulations.

You might be interested in
Simplify.<br> (-3.9) + (6.01) - (-7.423)<br> -5.513.<br> 2.487.<br> 9.533.
lianna [129]
First, since we must follow PEMDAS, we need to do the operation that is first, which is addition. 

-3.9 + 6.01  ← Adding a negative means subtracting, then giving the sign of the bigger number.

So now we solved those and we got this answer: 2.11

Now, we need to subtract and re-write the expression.

2.11 - (-7.423) = 2.11 + 7.423= 9.533

Ok....so now we have our final answer, and we have the choices above.

The only answer that matches ours is the last one.

Final answer: 9.533

Hope I helped ^_^

4 0
3 years ago
Read 2 more answers
What is an easy method to workout 35% of 70
dimulka [17.4K]

Step-by-step explanation:

70 \times  \frac{35}{100}  = 24 .5

7 0
2 years ago
Read 2 more answers
A line passes through the points (–6, 4) and (–2, 2). What is the equation of the line?
irga5000 [103]

I forgot how to find the y intercept but the slope is -2/4

6 0
3 years ago
Read 2 more answers
On monday there were 92 fish in the fish tank on tuesday 4 fish were sold on wednesday 1 fish was sold on thursday 4fish were ad
Julli [10]
Monday=92
Tuesday=88
Wednesday=87
Thursday=91
Friday=88
There are 88 fish remaining
7 0
3 years ago
Mrs. Powell has $800 invested in stocks and $500 invested in a Certificate of Deposit. The CD has an interest rate twice as grea
Mashutka [201]
Let's use the variable "r" to represent the investment rate of the stocks:
2r(500) + r(800) = 45
1000r + 800r = 45
1800r = 45
r = 0.025
2r = 0.05
The $500 is invested at 5%
7 0
3 years ago
Read 2 more answers
Other questions:
  • Polygon ABCDE is reflected across the x-axis to form polygon A′B′C′D′E′. Then polygon A′B′C′D′E′ is dilated by a scale factor of
    12·2 answers
  • Which of the following values is a solution of 12.6 less than or equal to 3x
    13·1 answer
  • I NEED THIS ASAP HELP
    11·1 answer
  • Which of the following equations represents a line with a negative slope and a negative y-intercept?
    14·1 answer
  • Help please!!!!!<br> Geometry
    15·1 answer
  • Anyone know how to find the area with the missing hypotenuse? Thank you!!!
    10·1 answer
  • Uhmm...help please :&lt; i'll give brainliest to whoever answers all three
    9·1 answer
  • Find the value of k.<br> 62°<br> 45°<br> k°
    6·1 answer
  • What is each measure and what does x equal
    10·1 answer
  • Pls help quick<br><br>Add<br>1. x³-2x²y+3xy²-y²,2x³-5xy²+3x²y-4y³​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!