Answer:
The  90 % confidence  interval  for the mean population is (11.176  ; 20.824 )
Rounding to at least two decimal places would give 11.18 , 20.83 
Step-by-step explanation:
Mean = x`= 16 miles per hour
standard deviation =s= 4.1 miles per hour
n= 4
 =  4.1/√4= 4.1/2= 2.05
  =  4.1/√4= 4.1/2= 2.05
1-α= 0.9
degrees of freedom =n-1=  df= 3
∈ ( estimator  t with 90 % and df= 3 from t - table ) 2.353
 Using Students' t - test 
x`±∈ * 
Putting values 
16 ± 2.353 * 2.05
= 16 + 4.82365
20.824  ;        11.176
The  90 % confidence  interval  for the mean population is (11.176  ; 20.824 ) 
Rounding to at least two decimal places would give 11.18 , 20.83
 
        
                    
             
        
        
        
Answer:
53.9
Step-by-step explanation:
you add all of the sides up
 
        
                    
             
        
        
        
Answer:
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
Step-by-step explanation:
We have that to find our  level, that is the subtraction of 1 by the confidence interval divided by 2. So:
 level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of  .
.
So it is z with a pvalue of  , so
, so 
Now, find the margin of error M as such

In which  is the standard deviation of the population and n is the size of the sample.
 is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm
The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
 
        
             
        
        
        
Answer:


Step-by-step explanation:
Trapezoid ABCD is isosceles trapezoid, because AB = CD (given). In isosceles trapezoid, angles adjacent to the bases are congruent, then
Since BK ⊥ AD, the triangle ABK is right triangle. In this triangle,  AB = 8, AK = 4. Note that the hypotenuse AB is twice the leg AK:
 
 
If in the right triangle the hypotenuse is twice the leg, then the angle opposite to this leg is 30°, so, 

Since BK ⊥ AD, then BK ⊥ BC and

Thus,

Now,
