Calculating Expected Value for Discrete Distributions Quiz

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| Questions: 20 | Updated: Nov 16, 2025
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1) In a batch of 500 items, approximately how many total defects should the inspector expect to find?

Explanation

0.42 × 500 = 210.

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About This Quiz
Calculating Expected Value For Discrete Distributions Quiz - Quiz

This quiz will help you calculate expected values for discrete distributions. It includes problems involving random variables such as arcade tickets, raffles, dice rolls, and defects per item, helping you understand the expected value's role in evaluating and comparing scenarios.

2)
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2) If the company’s goal is E[defects] < 0.30 per item, is this goal currently being met?

Explanation

Expected defects = 0.42 > 0.30.

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3) A game costs $3 to play. P($10)=0.2, P($0)=0.8. What is the expected net gain/loss per game?

Explanation

Expected prize = 2; net = 2 − 3 = −1.

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4) Which statement about expected value is TRUE?

Explanation

Expected value is the long-run average result over many trials.

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5) What is the expected value of points per spin?

Explanation

E(X) = 3.0.

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6) After 200 spins, approximately how many total points should a player expect to accumulate?

Explanation

3 × 200 = 600 points.

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7) For random variable Z: P(Z=−2)=0.3, P(Z=0)=0.4, P(Z=4)=0.3. What is E(Z)?

Explanation

E(Z)=0.6.

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8) A student calculates E(X)=7.8 for a discrete random variable. Which statement is most accurate?

Explanation

Expected value can be any real number and represents the mean.

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9) What is the expected value (mean) of tickets won per game?

Explanation

E(X) = 0·0.35 + 5·0.30 + 10·0.20 + 20·0.10 + 50·0.05 = 8 tickets.

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10) If a player plays this game 100 times, approximately how many total tickets should they expect to win?

Explanation

Expected tickets per game = 8. For 100 games: 8 × 100 = 800 tickets.

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11) Which interpretation best describes the expected value in this context?

Explanation

Expected value is the long-run average number of tickets per game over many plays.

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12) What is the probability of winning more tickets than the expected value in a single game?

Explanation

More than 8 tickets means 10, 20, or 50. P = 0.20 + 0.10 + 0.05 = 0.35.

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13) A random variable X has: P(X=2)=0.4, P(X=5)=0.3, P(X=8)=0.3. What is E[X]?

Explanation

E(X) = 2·0.4 + 5·0.3 + 8·0.3 = 4.7.

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14) A fair six-sided die is rolled. What is the expected value of the roll?

Explanation

E = (1+2+3+4+5+6)/6 = 3.5.

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15) What is the expected value of a single raffle ticket (prize winnings only)?

Explanation

Expected prize = $3.50.

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16) What is the expected net gain (or loss) for a person who buys one ticket?

Explanation

Expected prize = 3.50, cost = 5 → net = −1.50.

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17) If someone buys 10 tickets, what is their expected net gain or loss?

Explanation

Net loss per ticket = $1.50 → 10 × 1.50 = $15 loss.

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18) A distribution has E(X)=12. If each value of X is multiplied by 3, what is the new expected value?

Explanation

3 × 12 = 36.

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19) A random variable Y has E(Y)=8. If 5 is added to each value, what is the expected value of the new distribution?

Explanation

8 + 5 = 13.

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20) What is the expected number of defects per item?

Explanation

E(X)=0.42.

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In a batch of 500 items, approximately how many total defects should...
If the company’s goal is E[defects] < 0.30 per item, is this goal...
A game costs $3 to play. P($10)=0.2, P($0)=0.8. What is the expected...
Which statement about expected value is TRUE?
What is the expected value of points per spin?
After 200 spins, approximately how many total points should a player...
For random variable Z: P(Z=−2)=0.3, P(Z=0)=0.4, P(Z=4)=0.3. What is...
A student calculates E(X)=7.8 for a discrete random variable. Which...
What is the expected value (mean) of tickets won per game?
If a player plays this game 100 times, approximately how many total...
Which interpretation best describes the expected value in this...
What is the probability of winning more tickets than the expected...
A random variable X has: P(X=2)=0.4, P(X=5)=0.3, P(X=8)=0.3. What is...
A fair six-sided die is rolled. What is the expected value of the...
What is the expected value of a single raffle ticket (prize winnings...
What is the expected net gain (or loss) for a person who buys one...
If someone buys 10 tickets, what is their expected net gain or loss?
A distribution has E(X)=12. If each value of X is multiplied by 3,...
A random variable Y has E(Y)=8. If 5 is added to each value, what is...
What is the expected number of defects per item?
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