Question

In a company dedicated to packaging beer in 750 mL containers, a normal distribution is handled in its packaging process, which registers an average of 745 mL and a standard deviation of 8 mL. Determine: a) The probability that a randomly selected container exceeds 765 mL of beer b) The probability that the beer content of a randomly selected container is between 735 and 755 mL.

257

likes
1284 views

Answer to a math question In a company dedicated to packaging beer in 750 mL containers, a normal distribution is handled in its packaging process, which registers an average of 745 mL and a standard deviation of 8 mL. Determine: a) The probability that a randomly selected container exceeds 765 mL of beer b) The probability that the beer content of a randomly selected container is between 735 and 755 mL.

Expert avatar
Darrell
4.5
63 Answers
To solve this problem, we will use the properties of the normal distribution.

a) To find the probability that a randomly selected container exceeds 765 mL of beer, we need to calculate the z-score corresponding to 765 mL using the formula:

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

where X is the value we are interested in (765 mL), μ is the mean (745 mL), and σ is the standard deviation (8 mL). Substituting these values, we get:

z = \frac{{765 - 745}}{{8}} = \frac{{20}}{{8}} = 2.5

Next, we need to find the area under the normal curve to the right of the z-score of 2.5. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we find that the area to the right of 2.5 is approximately 0.0062.

Therefore, the probability that a randomly selected container exceeds 765 mL of beer is approximately 0.0062.

b) To find the probability that the beer content of a randomly selected container is between 735 and 755 mL, we need to calculate the z-scores corresponding to 735 mL and 755 mL.

For 735 mL:
z_1 = \frac{{735 - 745}}{{8}} = \frac{{-10}}{{8}} = -1.25

For 755 mL:
z_2 = \frac{{755 - 745}}{{8}} = \frac{{10}}{{8}} = 1.25

Next, we need to find the area under the normal curve between these two z-scores. We can subtract the area to the left of -1.25 from the area to the left of 1.25. Again, we can use a standard normal distribution table or a calculator to find these areas.

Using a standard normal distribution table, we find that the area to the left of -1.25 is approximately 0.1056, and the area to the left of 1.25 is approximately 0.8944.

Therefore, the probability that the beer content of a randomly selected container is between 735 and 755 mL is approximately 0.8944 - 0.1056 = 0.7888.

Answer:
a) The probability that a randomly selected container exceeds 765 mL of beer is approximately 0.0062.
b) The probability that the beer content of a randomly selected container is between 735 and 755 mL is approximately 0.7888.

Frequently asked questions (FAQs)
What is the amplitude, period, and vertical asymptotes of the function f(x) = cot(x)?
+
Math Question: Convert the number 2,500,000,000,000,000 into scientific notation.
+
What is the solution to 3x - 5 < 10?
+
New questions in Mathematics
-6(3x-4)=-6
-8+3/5
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
Determine the equations of the lines that pass through the following points P1 (2;-1) and p2 (4;-1)
Derivative of x squared
4x-3y=5;x+2y=4
A job takes 9 workers 92 hours to finish. How many hours would it take 5 workers to complete the same job?
Divide 22 by 5 solve it by array and an area model
7/6-(-1/9)
The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?
The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. a) What is the amount of VAT paid by the hotel for one
Calculate the value of a so that the vectors (2,2,−1),(3,4,2) and(a,2,3) are coplanar.
Use linear approximation to estimate the value of the sine of 31o.
TEST 123123+123123
A natural gas company has a fixed rate of 1,320 pesos plus 1,590 pesos per cubic meter of gas consumed monthly per customer. Indicate the cost function to determine the value in pesos of the cubic meters of gas consumed in a month per customer. How much did a customer who consumed 18 cubic meters of gas pay? If a customer paid 34,710 pesos, how many cubic meters of gas did he consume?
(6²-14)÷11•(-3)
A post office has three categories of letters: 60% are from businesses, 30% are individual mail, and the remaining 10% are government mail. 5% of the letters from businesses have address errors, 10% of the individual mail has address errors, while 1% of the government mail has address errors. If we receive a letter with an address error, what is the probability that it is individual mail?"
The inner radius of a spherical ball is 13 cm. How many liters of air are in it? Justify your answer!
Hola👋🏻 Toca en "Crear Nueva Tarea" para enviar tu problema de matemáticas. ¡Uno de nuestros expertos comenzará a trabajar en ello de inmediato!
Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2