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Travka [436]
2 years ago
13

The Federal Government is stepping up efforts to reduce average response times of fire departments to fire calls. Nationwide, th

e distribution of average response times to fire calls follows a normal distribution with a mean of 12.8 minutes and a standard deviation of 3.7 minutes. The fastest 20% of fire departments will be singled out for a special safety award. How fast must a fire department be in order to qualify for the special safety award
Mathematics
1 answer:
TiliK225 [7]2 years ago
7 0

Answer: in order to qualify, the time must be at least 15.93 minutes

Step-by-step explanation:

Let x be a random variable representing the average response times of fire departments to fire calls. Since it follows a normal distribution, we will determine the z score by applying the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

From the information given,

µ = 12.8 minutes

σ = 3.7 minutes

in order to qualify for the special safety award, the probability value would be to the right of the z score corresponding to 80%

The z score corresponding to 80% on the normal distribution table is 0.845

Therefore,

0.845 = (x - 12.8)/3.7

0.845 × 3.7 = x - 12.8

3.13 = x - 12.8

x = 12.8 + 3.13 = 15.93

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ladessa [460]

Answer:

The area of the country is 17 square miles

Step-by-step explanation:

To calculate the population density of the country. We employ the use of a mathematical formula. This can easily be obtained from the units of the density

The population density = Population of the country/area of the country

Since we are to calculate the area of the country, the equation becomes

Area of country = Population of country/population density of country

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A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height
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General Idea:

Domain of a function means the values of x which will give a DEFINED output for the function.

Applying the concept:

Given that the x represent the time in seconds, f(x) represent the height of food packet.

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The height of the food packet cannot be a negative value, so

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The possible solutions of the above inequality are given by the intervals (-\infty , -2], [-2,2], [2,\infty ). We need to pick test point from each possible solution interval and check whether that test point make the inequality (x+200)(x-200)\leq 0 true. Only the test point from the solution interval [-200, 200] make the inequality true.

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But we already know x should be positive, because time cannot be negative.

Conclusion:

Domain of the given function is 0\leq x\leq 200

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