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Alex73 [517]
3 years ago
12

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and th

e time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.8 minutes and a standard deviation of 1.9 minutes. For a randomly received emergency call, find the following probabilities. (a) the response time is between 5 and 10 minutes
(b) the response time is less than 5 minutes


(c) the response time is more than 10 minutes
Mathematics
1 answer:
Marizza181 [45]3 years ago
4 0

Answer:

\mu = 8.8\\\sigma = 1.9

Now we are supposed to find probabilities that the response time is between 5 and 10 minutes i.e P(5<x<10)

Formula : z= \frac{x-\mu}{\sigma}

at x = 5

z= \frac{5-8.8}{1.9}

z=-2

at x = 10

z= \frac{10-8.8}{1.9}

z=0.6315

P(-2<z<0.6315)=P(z<0.6315)-P(z<-2)

Refer the z table

P(-2<z<10)=0.7357-0.0228=0.7129

So, the probability that response time is between 5 and 10 minutes  is 0.7129

b)the response time is less than 5 minutes

at x = 5

z= \frac{5-8.8}{1.9}

z=-2

P(x<5)=P(z<-2)=0.0228

So, the probability that  the response time is less than 5 minutes is 0.0228

c)the response time is more than 10 minutes

at x = 10

z= \frac{10-8.8}{1.9}

z=0.6315

P(x>10) = 1-P(x<10) = 1-P(z<0.63) = 1-0.7357 = 0.2643

So, The probability that  the response time is more than 10 minutes is 0.2643

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A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car
Artyom0805 [142]

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Therefore $98 is be charged a bus containing 30 people.

Step-by-step explanation:

Given that,

A state park charges an entrance fee based on the number of people in vehicle.

Let the entry fee for the vehicle be E and entry fee for each person be x.

Then

C= E+(P×x)

C= Total charge in $

E= entry fee for a vehicle

P=No. of person

x= Entry charge per person.

Given A car containing 2 people charged $14

C=$14, P=2

∴14= E+(2× x)

⇒E+2x=14.....(1)

Again A car containing 4 people charged $20

C=$20, P=4

∴20= E+(4× x)

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Subtract (1) from (2), we get

E+4x-(E+2x)= 20-14

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Putting the value of x in equation (1)

E+(2×3)=14

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⇒E=8

Therefore E=$8 and x=$3

Next we check whether our assumption is correct or wrong. Putting the value of E and x for third case

Here P= 8

Therefore C= E+(P×x)

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Therefore our assumption is correct.

Now C=? , P= 30

The charged for the 30 people is

C= $[8+(30×3)]

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Therefore $98 is be charged a bus containing 30 people.

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3 years ago
A regular polygon has a perimeter of 40 cm and a apothem of 6 cm. find the polygons area
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Answer:

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