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
s2008m [1.1K]
3 years ago
15

4- A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produ

ced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.
Mathematics
1 answer:
galben [10]3 years ago
7 0

Answer:

\\ \mu = 118\;grams\;and\;\sigma=30\;grams

Step-by-step explanation:

We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find \\ \mu\;and\;\sigma.

<h3>First Case: items from 100 grams to the mean</h3>

For finding probabilities that corresponds to z-scores, we are going to use here a <u>Standard Normal Table </u><u><em>for cumulative probabilities from the mean </em></u><em>(Standard normal table. Cumulative from the mean (0 to Z), 2020, in Wikipedia) </em>that is, the "probability that a statistic is between 0 (the mean) and Z".

A value of a z-score for the probability P(100<x<mean) = 22.57% = 0.2257 corresponds to a value of z-score = 0.6, that is, the value is 0.6 standard deviations from the mean. Since this value is <em>below the mean</em> ("the items produced weigh between 100 grams up to the mean"), then the z-score is negative.

Then

\\ z = -0.6\;and\;z = \frac{x-\mu}{\sigma}

\\ -0.6 = \frac{100-\mu}{\sigma} (1)

<h3>Second Case: items from the mean up to 190 grams</h3>

We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.

Then

\\ z =2.4\;and\; z = \frac{x-\mu}{\sigma}

\\ 2.4 = \frac{190-\mu}{\sigma} (2)

<h3>Solving a system of equations for values of the mean and standard deviation</h3>

Having equations (1) and (2), we can form a system of two equations and two unknowns values:

\\ -0.6 = \frac{100-\mu}{\sigma} (1)

\\ 2.4 = \frac{190-\mu}{\sigma} (2)

Rearranging these two equations:

\\ -0.6*\sigma = 100-\mu (1)

\\ 2.4*\sigma = 190-\mu (2)

To solve this system of equations, we can multiply (1) by -1, and them sum the two resulting equation:

\\ 0.6*\sigma = -100+\mu (1)

\\ 2.4*\sigma = 190-\mu (2)

Summing both equations, we obtain the following equation:

\\ 3.0*\sigma = 90

Then

\\ \sigma = \frac{90}{3.0} = 30

To find the value of the mean, we need to substitute the value obtained for the standard deviation in equation (2):

\\ 2.4*30 = 190-\mu (2)

\\ 2.4*30 - 190 = -\mu

\\ -2.4*30 + 190 = \mu

\\ \mu = 118

You might be interested in
A baby elephant weighs 200 pounds at birth. Seven years later, the elephant's weight is 3,000 pounds.
almond37 [142]
What exactly is your question?
4 0
3 years ago
To join a local square dancing group, Jan has to pay a $100 sign-up fee plus $25 per month. Write an equation for the cost (y) b
klasskru [66]

Answer:

y = $100 + $25x

Step-by-step explanation:

y is the total cost

x is the number of months

The sign up fee is $100.

Each month would cost an additional $25 per month.

The total cost then would be the sign up fee plus the $25 for each month. Since we do not know the number of months, we will assign x.

So the equation would be:

y = $100 + $25x

3 0
3 years ago
PLEASE ANSWER!!! A certain transformation moves a line segment as follows: Pt. A (2, 1) moves to A' (2, -1) and Pt. B (5, 3) to
worty [1.4K]

Answer: I believe this is a reflection

Step-by-step explanation: I think this is a reflection because the points are flipping to the exact opposite y coordinate.

Hope this helps.

3 0
3 years ago
Read 2 more answers
8 miles in 0.5 hour what rate in miles per hour
yan [13]
In this question it is already given that a person travels 8 miles in 0.5 hours. This is enough information to get to the required answer. Let us first write down all the information's that are already given in the question.
In 0.5 hours the person covers a distance = 8 miles
Then
In 1 hour the person covers a distance of = 8/0.5 miles
                                                                   = 16 miles
So the speed of the person in miles per hour = 16/1 miles/hour
                                                                         = 16 miles per hour
8 0
2 years ago
Read 2 more answers
Given the equation,D=m/v. If D2/3 = and v = m + 1, then m = <br> 1<br> 2<br> -3
Yuliya22 [10]
The answer is probably m=2 
7 0
3 years ago
Read 2 more answers
Other questions:
  • The scale of a map is 1 inch to 15 miles. It is about 75 miles between two cities. How many inches should separate the cities on
    14·1 answer
  • using the foil method multiply (x2-7)(x2-4) then add any like terms and write polynomial in standard form. Show your work. Any b
    14·1 answer
  • Beau buys a 3-pound bag of trail mix for a hike. He wants to make one-ounce bags for his friends with whom he is hiking. How man
    7·2 answers
  • A triangle with side lengths 33 feet, 56 feet and 65 feet is a right triangle.
    11·2 answers
  • A scientist studied the migration patterns of two types of whales.
    9·1 answer
  • Find x. Round your answer to the nearest tenth. BRANLIEST ASAP TY!!​
    7·2 answers
  • A x + b y = c what are the variables?
    5·2 answers
  • In the forest were lions and tigers and bears. The ratio of lions to tigers was 4 to 5. The ratio of tigers to bears was 3 to 5.
    13·2 answers
  • Mrs. Lynch has noted that 7 out of every 10 pieces of mail she gets are junk mail. What percent of her mail is junk?
    7·2 answers
  • Solve the equation for x.​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!