Probability distributions, expected value, and the spread of a random variable

Answer Key - Grade 11 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Table: x = 0, 1, 2, 3; P(x) = 0.2, 0.4, 0.3, 0.1. Bo's table gives the distribution of the number of goals the class team scores in a game. To the nearest hundredth, what is its standard deviation?

   0.9
2. 2.

   Table: x = 1, 2, 3, 4; P(x) = 0.4, 0.1, 0.1, 0.4. Esme's table gives the distribution of the number of pages a printer jams on in a long print job. To the nearest hundredth, what is its standard deviation?

   1.36
3. 3.

   Table: x = 0, 1, 2; P(x) = 0.49, 0.42, 0.09. Jun's table gives the distribution of the free throws made in 2 tries by a practice shooter. To the nearest hundredth, what is its standard deviation?

   0.65
4. 4.

   Kira's table gives the distribution of the points a team earns for one answer in a quiz game. To the nearest hundredth, what is its standard deviation?

   7.81
5. 5.

   x = 10, ?, 50; P(x) = 0.5, 0.4, 0.1. Noah's distribution for the points a quiz answer earns has expected value 22, but one value is missing. What is the missing value?

   30
6. 6.

   x = 2, 5, ?; P(x) = 0.6, 0.3, 0.1. Ren's distribution for the minutes a slide line takes has expected value 3.6, but one value is missing. What is the missing value?

   9
7. 7.

   Tala compares the distributions of minutes late for two bus routes. Both balance at 5. Which statement is true?

   • Both have the same spread, because the balance points match
   • Route B has more spread
   • Route A has more spread
8. 8.

   Zee compares the distributions of the points for one turn in two class games. Both balance at 5. Which statement is true?

   • Game B has more spread
   • Game A has more spread
   • Both have the same spread, because the balance points match
9. 9.

   Esme compares the distributions of the minutes two school clocks run fast or slow. Both balance at 4. Which statement is true?

   • Clock A has more spread
   • Both have the same spread, because the balance points match
   • Clock B has more spread
10. 10.

    Jun compares the distributions of the grams over a label for two snack machines. Both balance at 6. Which statement is true?

    • Machine B has more spread
    • Both have the same spread, because the balance points match
    • Machine A has more spread