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just olya [345]
3 years ago
9

A city currently has 153 streetlights. As part of a urban renewal program, the city council has decided to

Mathematics
1 answer:
kiruha [24]3 years ago
5 0

Answer:

The explicit function is: P_x = 153+3x

And the number of lights after 33 weeks will be 252.

Step-by-step explanation:

Given that:

Total street lights = 153

Let x be the number of weeks

Then the number lights after x weeks will be 3x

This is a linear function where the y-intercept is 153 and slope is 3.

It can be written as: y = mx+b

The function is:

P_x = 153+3x

Putting the values for x will give us the number of total lights after that number of weeks.

To find, how many street lights were there at the end of 33rd week,

Putting x = 33

P_{33} = 153+ 3(33)\\= 153+99 = 252

Hence.

The explicit function is: P_x = 153+3x

And the number of lights after 33 weeks will be 252.

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3 years ago
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Q6. (15 points) IQ examination scores of 500 members of a club are normally distributed with mean of 165 and SD of 15.
melamori03 [73]

Answer:

a) 0.8413

b) 421

c) P_{95} = 189.675

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 165

Standard Deviation, σ = 15

We are given that the distribution of  IQ examination scores is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(IQ scores at most 180)

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P( x < 180) = P( z < \displaystyle\frac{180 - 165}{15}) = P(z < 1)

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P(x < 180) = 0.8413 = 84.13\%

b) Number of the members of the club have IQ scores at most 180

n = 500

\text{Members} = n\times \text{P(IQ scores at most 180)}\\= 500\times 0.8413\\=420.65 \approc 421

c) P(X< x) = 0.95

We have to find the value of x such that the probability is 0.95

P( X < x) = P( z < \displaystyle\frac{x - 165}{15})=0.95  

Calculation the value from standard normal z table, we have,  

P(z < 1.645) = 0.95

\displaystyle\frac{x - 165}{15} = 1.645\\\\x = 189.675  

P_{95} = 189.675

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The correct answer is
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