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Papessa [141]
2 years ago
8

Lamar and lawrence run a two-person lawn-care service. they have been caring for mr. johnson's very large lawn for several years

, and they have found that the time it takes lamar to mow the lawn itself is approximately normally distributed with a mean of 105 minutes and a standard deviation of 10 minutes. meanwhile, the time it takes for lawrence to use the edger and string trimmer to attend to details is also normally distributed with a mean of 98 minutes and a standard deviation of 15 minutes. they prefer to finish their jobs within 5 minutes of each other. what is the probability that this happens, assuming their finish times are independent?

Mathematics
2 answers:
Serggg [28]2 years ago
4 0

Answer:

0.2892

Step-by-step explanation:

Let X be the time for Lamar to finish and Y for Lawrence

Given that X is N(105, 10)

Y N(98,15)

consider the random variable x-y

Since x and y are independent we have

x-y is normal with mean = 105-98 =7

and variance of x-y = varx +vary

= 100+225 =325

STd dev = sq rt 325 =18.03

X-Y = U is N(7, 18.03)

Required probability

= P(|x-y|<5)=P(-5<U<5)

Convert to std normal variate Z

-5 becomes (-5-7)/18.03 =-0.67

5 becomes  (5-7)/18.03 =-0.11

Hence required prob

P(-0.67<Z<0.11) = 0.2454+0.0438

=0.2892

Naddik [55]2 years ago
3 0
The difference of finish times has a mean of
  μ = 105 -98 = 7 . . . . minutes
and a variance of
  σ² = 10² +15² = 325 . . . . minutes²

Using a probability calculator, we find the probability to be
  p(-5 < x < 5) ≈ 0.2030

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Lana71 [14]

Answer:

405

Step-by-step explanation:

To find sample size, use the following equation, where n = sample size, za/2 = the critical value, p = probability of success, q = probability of failure, and E = margin of error.

n=\frac{(z_{\frac{\alpha }{2} })^{2} *p*q  }{E^2}

The values that are given are p = 0.84 and E = 0.03.

You can solve for the critical value which is equal to the z-score of  (1 - confidence level)/2.  Use the calculator function of invNorm to find the z-score.  The value will given with a negative sign, but you can ignore that.

(1 - 0.9) = 0.1/2 = 0.05

invNorm(0.05, 0, 1) = 1.645

You can also solve for q which is 1 - p.  For this problem q = 1 - 0.84 = 0.16

Plug the values into the equation and solve for n.

n =\frac{(1.645)^2*0.84*0.16}{(0.03)^2}\\n= 404.0997333

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6 0
2 years ago
The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is .
Readme [11.4K]

Answer:

(-21,-19)

\sqrt{849}

Standard form

Step-by-step explanation:

We are given the equation of circle

x^2+y^2+42x+38y-47=0

General equation of circle:

x^2+y^2+2gx+2fy+c=0

Centre: (-g,-f)

Radius: \sqrt{g^2+f^2-c}

Compare the equation to find f, g and c from the equation

g\rightarrow 21

f\rightarrow 19

c\rightarrow -47

Centre: (-21,-19)

Radius (r) =\sqrt{21^2+19^2+47}=\sqrt{849}

Standard form of circle:

(x+21)^2+(y+19)^2=849

The centre of circle at the point (-21,-19) and its radius is \sqrt{849}.

The general form of the equation of a circle that has the same radius as the above circle is standard form.

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Answer:

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