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uranmaximum [27]
2 years ago
10

Suppose that a jewelry store tracked the amount of emeralds they sold each week to more accurately estimate how many emeralds to

keep in stock. At the end of one year, the store used the weekly sales information to construct a 95% confidence interval for the mean number of emeralds sold per week. The confidence interval they calculated was ( 3.25 , 4.51 ) . Use the confidence interval to find the point estimate for the mean and the margin of error. Give your answers precise to two decimal places.
Mathematics
1 answer:
Ratling [72]2 years ago
8 0

Answer: point estimate = 3.88

Margin of error = 0.63

Step-by-step explanation:

Confidence interval is written in the form,

(Point estimate - margin of error, Point estimate + margin of error)

The sample mean, x is the point estimate for the population mean. Let m represent the margin of error. Since the confidence interval is given as (3.25 , 4.51), it means that

x - m = 3.25

x + m = 4.51

Adding both equations, it becomes

2x = 7.76

x = 7.76/2

x = 3.88

Substituting x = 3.88 into x + m = 4.51, it becomes

3.88 + m = 4.51

m = 4.51 - 3.88

m = 0.63

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postnew [5]
In order to solve this, you have to set up a systems of linear equations.

Let's say that children = c and adults = a

30a + 12c = 19,080
a + c = 960

I'm going to show you how to solve this system of linear equations by substitution, the easiest way to solve in my opinion.

   a + c = 960 
       - c    -    c
 ---------------------- ⇒ Step 1: Solve for either a or c in either equation.
   a = 960 - c 



20(960 - c)+ 12c = 19,080
19,200 - 20c + 12c = 19,080
   19,200 - 8c = 19,080
 - 19,200         - 19,200
---------------------------------- ⇒ Step 2: Substitute in the value you got for a or c
         8c = -120                    into the opposite equation.                                                
       ------  ---------
          8         8
 
         c = -15



30a + 12(-15) = 19,080
   30a - 180 = 19,080
          + 180  +     180
 -------------------------------
   30a = 19,260
  -------   -----------
    30          30
     
       a = 642
__________________________________________________________

I just realized that there can't be a negative amount of children, so I'm sorry if these results are all wrong. 


7 0
2 years ago
Read 2 more answers
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viktelen [127]

Answer:

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2

1

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Step-by-step explanation:

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2 years ago
Suppose X is the breaking strength (newtons) of a material, and X is normally distributed with
Veronika [31]

Answer:

a) 0.997 is the  probability that the breaking strength is at least 772 newtons.

b) 0.974  is the probability that this material has a breaking strength of at least 772 but not more  than 820    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 800 newtons

Standard Deviation, σ = 10 newtons

We are given that the distribution of  breaking strength is a bell shaped distribution that is a normal distribution.

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z_{score} = \displaystyle\frac{x-\mu}{\sigma}

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b) P( breaking strength of at least 772 but not more  than 820)

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P(772 \leq x \leq 820) = 97.4\\%

0.974  is the probability that this material has a breaking strength of at least 772 but not more  than 820.

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