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
Degger [83]
3 years ago
13

If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi

ll be 55.4 gallons or more? Show your work?
Mathematics
1 answer:
Sophie [7]3 years ago
8 0

Answer:

P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)

P(Z>0.8)=1-P(Z\leq 0.8)

P(Z>0.8)=1-0.788=0.212

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long  trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly,  the actual volume of oil loaded into each barrel by the filling equipment at the port is  approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5  gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

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".  

Solution to the problem

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

X \sim N(55,0.5)  

Where \mu=55 and \sigma=0.5

We are interested on this probability

P(X>55.4)

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>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)

And we can find this probability using the complement rule:

P(Z>0.8)=1-P(Z\leq 0.8)

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(Z>0.8)=1-0.788=0.212

You might be interested in
2x-ay=3<br><br>8x-12y=b I'm supposed to find what a-b equals.
PolarNik [594]

Answer:

2

Step-by-step explanation:

3 0
3 years ago
Your car invoice reads: “Price $1,492.50, dealer preparation $45.00, transportation $54.50, undercoat $148.80, 60-day guarantee
Maurinko [17]

Answer:$2,074.53

Step-by-step explanation:

Final cost will be calculated as the sum of each expense stated on the invoice, which is $1,492.50 + $45 + $54.50+ $148.80 + $95 + $238.73 = $2,074.53

Final cost = $2,074.53, i hope this helps, please mark as brainliest answer.

7 0
3 years ago
What is thirty seven squared?
SSSSS [86.1K]
Ur answer is 1369 that is ur answer hope it helped and hope u pass
 


4 0
3 years ago
Read 2 more answers
What is the solution to this equation?<br> (1/4)x+1 =32<br> A. -7/2<br> B. -2<br> C. 3/2<br> D. 2
ANEK [815]
(1/4)x+1=32
(1/4)x=31
X=31*4
X=124
7 0
2 years ago
Need Help on this, First RIGHT answer gets brainliest :)
yaroslaw [1]
The answer is 50% as half the circle is shaded!
7 0
3 years ago
Read 2 more answers
Other questions:
  • Gender in the Population of Part-time College Students According to a 2010 report from the American Council on Education, female
    12·1 answer
  • What is 4.75 as a fraction?
    8·2 answers
  • Jodi and mariah are sisters. jodi is three years older than mariah. using one variable, write an expression to represent the sum
    11·1 answer
  • You toss n balls into n bins. for each toss there is a 1/n probability that the ball you toss lands in any one of the bins. afte
    7·1 answer
  • X^2- 4x- 6y- 14=0 in standard parabola form.
    13·1 answer
  • (3 * 2)2/6 - 5 + (4 - 1)2?
    14·2 answers
  • I<br> Need. Dis quickly my sis will get mad
    13·1 answer
  • Okie hat are the solutions of X^2-2x+5=0
    6·1 answer
  • Question five for geometry quiz
    7·1 answer
  • Please help asap! really important!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!