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3 years ago

The diameter of a circular table is 6 feet. Which of the following is closest to the area of the tabletop

Mathematics

2 answers:

Ivahew [28]3 years ago

6 0

So if you do 6(pi) then you should get 18.84

andrew11 [14]3 years ago

5 0

The area is aproximately 28.27 feet. The formula for circular area is A=πr2 (pi times radius squared)

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mylen [45]

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(a) The standard deviation of your waiting time is 4.33 minutes.

(b) The probability that you will have to wait more than 2 standard deviations is 0.4227.

Step-by-step explanation:

Let X = the waiting time for the bus at the parking lot.

The random variable X is uniformly distributed with parameters a = 0 to b = 15.

The probability density function of X is given as follows:

$f_{X}(x)=\frac{1}{b-a};\ a$

(a)

The standard deviation of a Uniformly distributed random variable is given by:

$SD=\sqrt{\frac{(b-a)^{2}}{12}}$

Compute the standard deviation of the random variable X as follows:

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$=\sqrt{\frac{225}{12}}$

$=\sqrt{18.75}\\=4.33$

Thus, the standard deviation of your waiting time is 4.33 minutes.

(b)

The value representing 2 standard deviations is:

$X=2\times SD=2\times4.33=8.66$

Compute the value of P (X > 8.66) as follows:

$P(X>8.66)=\int\limits^{10}_{8.66} {\frac{1}{15-0}}\, dx\\$

$=\frac{1}{15}\times \int\limits^{10}_{8.66} {1}\, dx\\$

$=\frac{1}{15}\times |x|^{15}_{8.66}\\$

$=\frac{15-8.66}{15}\\$

$=0.4227$

Thus, the probability that you will have to wait more than 2 standard deviations is 0.4227.

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