Resources

Resources

Identify discrete and continuous random variables

11

55

p.m., Thomas ties a weight to the minute hand of a clock. The clockwise torque applied by the weight (i.e. the force it applies on the clock's hand to move clockwise) varies in a periodic way that can be modeled by a trigonometric function.

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The torque peaks

15

minutes after each whole hour, when the minute hand is pointing directly to the right, at

3

\mathrm{Nm}

(Newton metre, the SI unit for torque). The minimum torque of

-3

\mathrm{Nm}

15

minutes before each whole hour, when the minute hand is pointing directly to the left.

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Find the formula of the trigonometric function that models the torque

\tau

applied by the weight

t

minutes after Thomas attached the weight. Define the function using radians.

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\tau(t)=\square

A craps player rolls two six-sided dice.

Y

is the distance between the centers of the two dice after they come to a rest.

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Is the random variable

Y

discrete or continuous?

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Z

is the length of a randomly chosen sidewalk.

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Is the random variable

Z

discrete or continuous?

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Y

is the time it takes a chef to cook a specific dish.

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Is the random variable

Y

discrete or continuous?

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A randomly chosen child repeatedly hits a piñata.

Z

is the length of time it takes to break it open.

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Is the random variable

Z

discrete or continuous?

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A craps player rolls two six-sided dice.

X

is the distance between the centers of the two dice after they come to a rest.

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Is the random variable

X

discrete or continuous?

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A student repeatedly rolls a die.

Y

is the furthest distance away in which the die lands in the first ten rolls.

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Is the random variable

Y

discrete or continuous?

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4x

gives the perimeter of a square with a side length of

x

units. What is the perimeter of a square with a side length of

\frac{5}{7}

f(x)

is a continuous function such that

\int_{a}^{\infty}f(x)\,dx

a < b

\int_{b}^{\infty}f(x)\,dx

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For the following set of data, find the sample standard deviation, to the nearest thousandth.

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70,39,114,39,52,108,101

For the following set of data, find the sample standard deviation, to the nearest thousandth.

96,63,83,78,55,96,114,52

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of

22

minutes and a standard deviation of

3

minutes. If you visit that restaurant

37

times this year, what is the expected number of times that you would expect to wait between

19

23

minutes, to the nearest whole number?

g

be a continuous function on the closed interval

[-1,4]

g(-1)=-4

g(4)=1

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Which of the following is guaranteed by the Intermediate Value Theorem?

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1

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g(c)=-3

for at least one

c

-1

4

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g(c)=3

for at least one

c

-4

1

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g(c)=-3

for at least one

c

-4

1

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g(c)=3

for at least one

c

-1

4

Which of the following functions are continuous for all real numbers?

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g(x)=\ln (x)

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f(x)=\frac{1}{x}

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1

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g

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f

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g

f

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g

f

Which of the following functions are continuous at

x=-1

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g(x)=\sin (x+1)

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f(x)=\frac{1}{x-1}

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1

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g

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f

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g

f

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g

f

Y

is the number of desserts available in a randomly chosen restaurant.

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Is the random variable

Y

discrete or continuous?

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\text{[A]discrete}

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\text{[B]continuous}