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shtirl [24]
3 years ago
11

In a random sample of 8 people, the mean commute time to work was 36.5 minutes and the standard deviation was 7.4 minutes. A 98%

confidence interval using the t-distribution was calculated to be (28.7,44.3). After researching commute times to work, it was found that the population standard deviation is 8.7 minutes. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.The margin of error of u is ___A 98% confidence interval using the standard normal distribution is (__,__)Compare the results. Choose the correct answer below.a. the confidence interval found using the standard normal distribution has smaller lower and upper confidence interval limitsb. the confidence interval found using the standard normal distribution is wider than the confidence interval found using the students t-distributionc. the confidence interval found using the standard noraml distribution is the same as the confidence interval found using the students t-distributiond. the confidence interval found using the standard normal distrubution is narrower than the confidence interval found using the students t-distribution
Mathematics
1 answer:
ANEK [815]3 years ago
3 0

Answer:

Step-by-step explanation:

Given that

Sample size = n = 8: sample mean = 36.5 and s = sample std dev = 7.4 minutes

98% CI using t = (28.7, 44.3) with margin of error as 7.8

Now if sigma = population std dev is known we use Z critical value

Margin of error = 2.33*8.7/\sqrt 8 = 7.167

CI = (36.5 ±7.167)

This is not wider than that used using t distribution

The margin of error of u is ___7.167

98% confidence interval using the standard normal distribution is (29.333__,43.667__)

d)the confidence interval found using the standard normal distrubution is narrower than the confidence interval found using the students t-distribution

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Divide round your answer to the nearest hundredth 5608.67÷7
Likurg_2 [28]

Answer:

5608.67 ÷ 7 = 801.24

4 0
3 years ago
Create a list of steps, in order, that will solve the following equation 1/4(x+5)^2-1=3
julia-pushkina [17]

Answer:

either x = -1, or x = - 9

Step-by-step explanation:

given   \frac{1}{4} (x+5)^{2} -1=3

add one to both sides   \frac{1}{4} (x+5)^{2} =4

im not sure which one comes first. either you multiply both the x and the 5 in the parenthesis by \frac{1}{4}. or you square x and 5

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :   1/4*(x+5)^2-(4)=0  

Step by step solution :

Step  1  :

           1 /4

Equation at the end of step  1  :

  1                  

 (— • (x + 5)2) -  4  = 0  

  4                  

Step  2  :

Equation at the end of step  2  :

 (x + 5)2    

 ———————— -  4  = 0  

    4        

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

        4         4 • 4

   4 =  —  =  ———

        1            4  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+5)2 - (4 • 4)     x2 + 10x + 9

———————     ———————  =  ——

       4                        4      

Trying to factor by splitting the middle term

3.3     Factoring  x2 + 10x + 9  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +10x  its coefficient is  10 .

The last term, "the constant", is  +9  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 9 = 9  

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   10 .

     -9    +    -1    =    -10  

     -3    +    -3    =    -6  

     -1    +    -9    =    -10  

     1    +    9    =    10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  9  

                    x2 + 1x + 9x + 9

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+1)

             Add up the last 2 terms, pulling out common factors :

                   9 • (x+1)

Step-5 : Add up the four terms of step 4 :

                   (x+9)  •  (x+1)

            Which is the desired factorization

Equation at the end of step  3  :

 (x + 9) • (x + 1)

 —————————————————  = 0  

         4        

Step  4  :

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 (x+9)•(x+1)

 ——————————— • 4 = 0 • 4

      4      

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  (x+9)  •  (x+1)  = 0

Theory - Roots of a product :

4.2    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

4.3      Solve  :    x+9 = 0  

Subtract  9  from both sides of the equation :  

                     x = -9

Solving a Single Variable Equation :

4.4      Solve  :    x+1 = 0  

Subtract  1  from both sides of the equation :  

                     x = -1

Supplement : Solving Quadratic Equation Directly

Solving    x2+10x+9  = 0   directly  

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

6 0
3 years ago
Cuanto es 3/4 × 5/6 ​
marshall27 [118]

Answer:0.625 or 5/8

Step-by-step explanation:

6 0
3 years ago
Complete the solution of the equation find the value of y when x equals 2. -8x - 5y = -1
tatuchka [14]

Answer: y = -3

<u>Step-by-step explanation:</u>

-8x - 5y = -1

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       -5y = 8x  - 1

       <u> ÷-5 </u> <u> ÷-5</u>  <u>÷-5</u>

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       y(2) = -\frac{8}{5}(2) + \frac{1}{5}

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6 0
3 years ago
X varies directly with y. If x is 16 when y is 20, find x when y is 80.
Taya2010 [7]

Answer:

32

Step-by-step explanation:

16/20 reduces down to 2/5

set 2/5=x/80

cross multiply 160=5x

divide 32=x

check 2/5=32/80

32/80; 16/40; 8/20; 4/10; 2/5

yay 32 is the answer good luck :)

5 0
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