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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.

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