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Eleventh Grade (Grade 11) Statistics and Probability Concepts Questions

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Grade 11 Represent and Determine Probability CCSS: HSS-CP.B.9
At Karen's school, each locker comes with a lock that already has a combination. The locks use four numbers between 1 and 60 which aren't repeated. Karen is hoping that her locker combination has the numbers 4, 10, 22, and 50 which happen to have special significance for her. She doesn't care what order these numbers are in. She determines that there are [math]P(60,4)[/math] total possibilities for the locker combination, and [math]P(4,4)[/math] possibilities that include her numbers. Therefore, the probability that she gets her numbers is [math]2.1 xx 10^{-6}[/math]. Is she correct, and if not, why?
  1. No. Although justified in using permutations for the total number of possibilities, since order does matter, she should have used combinations to calculate the number of possibilities which include her numbers, since she doesn't care about the order for them. The probability should be [math](C(4,4)) / (P(60,4)) = 8.5 xx 10^{-8}[/math].
  2. No. Even though the end answer is correct, it is by chance. The total possibilities for locker combinations is [math]C(60,4)[/math] and the number of possibilities that include her numbers is [math]C(4,4)[/math]. This just happens to also equal [math]2.1 xx 10^{-6}[/math].
  3. No. The correct number of possibilities for the lock combination should be [math]60^4[/math]. Therefore, the probability would be [math](P(4,4)) / 60^4 = 1.9 xx 10^{-6}[/math].
  4. Yes. Karen's method is correct.
Grade 11 Represent and Determine Probability CCSS: HSS-CP.B.9
Given the letters A, B, E, L, S, T, what is the probability that a random assortment of these letters will result in the words "stable" or "tables"?
  1. [math]1.3 xx 10^{-1}[/math]
  2. [math]1.4 xx 10^{-3}[/math]
  3. [math]2.8 xx 10^{-3}[/math]
  4. [math]4.3 xx 10^{-5}[/math]
Grade 11 Represent and Determine Probability CCSS: HSS-CP.B.9
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.1
The shape that is made by a normal distribution of data is commonly referred to as
  1. a normal graph.
  2. a bell curve.
  3. a normal map.
  4. a deviation curve.
Grade 11 Bar Graphs
Grade 11 Represent and Determine Probability CCSS: HSS-CP.A.2
If you flip a coin 4 times, what is the probability you get heads, heads, tails, heads in that order?
  1. [math]1/8[/math]
  2. [math]1/2[/math]
  3. [math]1/16[/math]
  4. [math]1/32[/math]
  5. none of these are correct
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
Standard deviation is best described as
  1. the difference between the number and the mean.
  2. the sum of the differences between the numbers and the mean.
  3. the square root of the sum of the differences between the numbers and the mean squared and divided by the number of terms.
  4. the square root of the mean divided by the Z-Score times the sum of the numbers.
Grade 11 Represent and Determine Probability
Grade 11 Combinations and Permutations
To find the probability of two independent events occurring, you must
  1. multiply the elements together.
  2. determine the number of elements, then multiply.
  3. find the probability of each element, then multiply.
  4. divide the number of favorable outcomes by the number of total outcomes.
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