4.8 & 4.9 Mean and SD of Rand Var & Combining Random Variables

Match

Match the following

• Probability of spinning 1 and A

• Probability of spinning even and C

• Probability of spinning 7 and B

• Probability of spinning 9 and A

1/16

1/12

1/24

0

• 1/16

• 1/12

• 1/24

• 0

Multiple Choice

What are the key differences between discrete and continuous random variables?

• Discrete random variables can take on any value within a range.

• Continuous random variables can only take on specific values.

• Discrete random variables are countable, while continuous random variables are measurable.

• Both types of random variables are used in probability distributions.

Multiple Choice

The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W=7+2X. What are the mean and standard deviation of W?

• Mean = 31, Standard Deviation = 6
• Mean = 40, Standard Deviation = 2
• Mean = 25, Standard Deviation = 5
• Mean = 12, Standard Deviation = 3

Multiple Choice

When you add a positive constant to a random variable the effects on the random variables distribution are as follows:

• the shape is changed, the mean is increased by a value of "a" and the standard deviation is unchanged.

• the shape and standard deviation are unchanged and the mean is increased by a value of "a".

• all three aspects are unchanged

• the shape and mean are unchanged and the standard deviation is increased by a value of "a".

Open Ended

Compare the shape, center, and spread of the two probability distributions.

Multiple Choice

How does multiplying or dividing by a constant affect a random variable?

• It changes the shape of the distribution

• It only affects the mean

• It affects measures of center and spread

• It has no effect on the distribution

Multiple Choice

If 20 is added to the data set below, which statement will be true?
50, 55, 55, 60, 62

• The median will be 20

• The mode will increase

• The mean will increase

• The mean will decrease

Multiple Choice

If 20 is added to the data set below, which statement will be true?
50, 55, 55, 60, 62

• The median will be 20
• The mode will increase
• The mean will increase
• The mean will decrease

Multiple Choice

What are the means and standard deviations of the collected money (C) and profit (V) for Pete's Jeep Tours?

• Mean of C: $562.50, SD of C: $163.50; Mean of V: $462.50, SD of V: $163.50

• Mean of C: $500.00, SD of C: $150.00; Mean of V: $400.00, SD of V: $100.00

• Mean of C: $600.00, SD of C: $200.00; Mean of V: $500.00, SD of V: $150.00

• Mean of C: $550.00, SD of C: $160.00; Mean of V: $450.00, SD of V: $170.00

Multiple Choice

The number of DVDs rented daily at DVD rental machine has a mean of 134 with a standard deviation of 32.

The cost of the electricity to keep the DVD rental machine on is $1.45 per day. Each DVD rental increases the electricity cost by $0.02. What are the mean and standard deviation of the electricity cost per day?

• Mean = $4.13, Standard Deviation = $0.64

• Mean = $4.13, Standard Deviation = $1.77

• Mean = $4.13, Standard Deviation = $2.09

• Mean = $2.68, Standard Deviation = $0.64

• Mean = $2.68, Standard Deviation = $2.09

Multiple Choice

What are the mean and variance of T, where T = X + Y?

• Mean = 3.75, Variance = 1.090

• Mean = 3.10, Variance = 0.943

• Mean = 6.85, Variance = 2.033

• Mean = 4.85, Variance = 1.500

Multiple Choice

How many total passengers can Pete and Erin expect on a randomly selected day?

• 5.00

• 6.85

• 7.50

• 8.00

Multiple Choice

What are independent random variables?

• Variables that are dependent on each other

• Variables that do not affect each other

• Variables that are always equal

• Variables that are always different

Open Ended

What do you notice about the variance of T?

The number of calories in a 1-ounce serving of a certain breakfast

cereal is a random variable with mean 110 and standard deviation

10. The number of calories in a cup of whole milk is a random

variable with mean 140 and standard deviation 12. For breakfast,

you eat 1 ounce of the cereal with 1/2 cup of whole milk. Let T be

the random variable that represents the total number of calories in

this breakfast.

Multiple Choice

The number of calories in a 1-ounce serving of a certain breakfast

cereal is a random variable with mean 110 and standard deviation

10. The number of calories in a cup of whole milk is a random

variable with mean 140 and standard deviation 12. For breakfast,

you eat 1 ounce of the cereal with 1/2 cup of whole milk. Let T be

the random variable that represents the total number of calories in

this breakfast. The mean of T is

• 170
• 150
• 200
• 180

Multiple Choice

What is the variance of T if T = X + Y for two independent random variables X and Y?

• σ²T = σ²X + σ²Y

• σ²T = σ²X - σ²Y

• σ²T = σ²X * σ²Y

• σ²T = σ²X / σ²Y

Multiple Choice

The number of calories in a 1-ounce serving of a certain breakfast

cereal is a random variable with mean 110 and standard deviation

10. The number of calories in a cup of whole milk is a random

variable with mean 140 and standard deviation 12. For breakfast,

you eat 1 ounce of the cereal with 1/2 cup of whole milk. Let T be

the random variable that represents the total number of calories in

this breakfast. The standard deviation of T is

• 11.66
• 9.75
• 12.00
• 10.50

Multiple Choice

What is the variance of D when D = X - Y for any two independent random variables X and Y?

• Var(D) = Var(X) + Var(Y)

• Var(D) = Var(X) - Var(Y)

• Var(D) = Var(X) * Var(Y)

• Var(D) = Var(X) / Var(Y)

Multiple Choice

What is the probability that Mr. Starnes's tea will taste right if he likes between 8.5 and 9 grams of sugar?

• 0.8480

• 0.9772

• 0.1292

• 0.16

Multiple Choice

Multiplying a random variable by a positive constant "b" affects the distribution of the random variable as follows:

• the shape is unchanged, measures of center and spread, both, are multiplied by "b".

• the shape, measures of center and measures of spread are all multiplied by "b".

• the shape and measures of center are unchanged, the measures of center are multiplied by "b".

• there is no change in the distribution.

Multiple Choice

If X and Y are independent random variables, what is the relationship between their variances?

• Var(X^2 + Y^2) = Var(X) + Var(Y)

• Var(X^2 + Y^2) = Var(X) * Var(Y)

• Var(X^2 + Y^2) = Var(X) - Var(Y)

• Var(X^2 + Y^2) = Var(X) / Var(Y)

Multiple Choice

A discrete random variable X has the probability distributions shown in the table. Find the value of k. (Remember that a valid probability distribution must add up to 1)

• 1/3

• 7/12

• 1/12

• 1/4

Poll

How confident do you feel about this topic now?

• Very confident
• Somewhat confident
• Not confident