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Brilliant_brown [7]
3 years ago
10

Statistics please help I'm not good worth 50 points

Mathematics
1 answer:
mina [271]3 years ago
8 0

(a) I can't help you with using your calculator for this part, but if you have some familiarity with your device you can check your answer with mine.

The mean is simply the sum of all the house costs divided by the number of houses:

(75k + 75k + 150k + 155k + 165k + 203k + 750k + 755k)/8 = 291k

So the population mean is $291,000.

The population standard deviation is the square root of the population variance. To get the variance, you take the sum of all the squared differences between the cost and the mean cost, then divide that sum by the number of houses. That is,

[(75k - 291k)² + (75k - 291k)² + … + (755k - 291k)²]/8 = 581,286k

Note that the variances is measured in square dollars. Then the standard deviation is

√(581,286k) ≈ $762,421.1

(b) The median is just the price in the middle. There were 8 houses sold, so there are 2 "middle" prices. The median is the average of these:

(155k + 165k)/2 = 160k = $160,000

(c) Yes, the mode is the data that shows up most frequently. This happens at the lower end, with $75,000 appearing twice.

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T  =  1/2* (√4 + x²)  +( 15 - x )/3   Objective Function to minimize

b) V(min)  = 2.59 m/hr

Step-by-step explanation:

Let assume the boat is in Point A,  she lands in point B, and R  is the restaurant

Let call  x distance between the point O in  which perpendicular line from the boat get to shoreline, and the point were she land.

We know  distance is

d = v*t       ⇒  t = d/v

She rows at 2 miles/hr  and walk at 3 miles /hr

According to that she takes

c (hypotenuse) of right triangle  AOB/ 2 rowing

and  15 - x /3  walking

Total time is:

T  =  c/2  + ( 15-x )/3          c =√(2)² + x²     ⇒  T = [√(2)² + x²  ] /2  +  ( 15-x )/3  

T  =  1/2* (√4 + x²)  +( 15 - x )/3   (1)

And that is  the Objective function to minimize

a) Taking derivatives on both sides of the equation we get

T´(t)  =  x /( √4 + x²)  - 1/3    ⇒   T´(t)  = 0     x /( √4 + x²)  - 1/3 = 0

3*x - √( √4 + x²) = 0     ⇒  3*x  =  √( √4 + x²)

Squaring both sides

9x²  =  4 + x²     ⇒  8x²  = 4       x² = 1/2      x  =  0,70 miles

If we plug this value in the Objective function we will get the minimum time

1/2* (√4 + x²)  +( 15 - x )/3    ⇒ [√ 4  + 0,5] /2 +  14,3/3 = T (min)

T(min)  =  1.06 + 4.77  = 5.83 hr

Distance L (hypotenuse of right triangle AOR)

L = √(2)²  + (15)²   L  = 15,13 miles

And that distance have to be traveled at least in 5.83 hr rowing

Then  as  v = d/t      V(min)  =  15.13/ 5.83   ⇒    V(min)  = 2.59 m/hr

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