Year 12 in England

11th grade statistics and probability

8 11th grade statistics and probability skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.

Mixed review

Ten questions drawn from every skill below.

Print a review worksheet Riddle puzzle on screen Bingo

Permutations and combinations

CCSS HSS.CP.B.9

Example

In how many ways can 1st, 2nd, 3rd and 4th place be awarded among 7 runners?

7 × 6 × 5 × 4 = 840

Answer: 840

Builds on: Compound events and sample spaces

Leads to: Expected value, Binomial probability, Find a coefficient in a binomial expansion, Find probabilities using combinations

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The normal distribution (68–95–99.7 rule)

CCSS HSS.ID.A.4

Example

A variable is normally distributed with mean 103 and standard deviation 5. About what percentage of values lie between 98 and 108?

They are 1 standard deviation either side of the mean.
≈ 68%

Answer: 68

Builds on: Spread: standard deviation

Leads to: Combine regions of a normal curve with the 68–95–99.7 rule

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Calculate variance and standard deviation

CCSS HSS.ID.A.2England: A-level Statistics

Example

Find the variance of 27, 30, 31, 29, 28 (treat them as the whole population).

mean = 29
((−2)² + (−1)² + 0² + 1² + 2²) ÷ 5 = 2

Answer: 2

Builds on: Spread: standard deviation

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Calculate and use z-scores

CCSS HSS.ID.A.4England: A-level Statistics

Example

A test has mean 66 and standard deviation 9. Find the z-score of a mark of 93.

(93 − 66) ÷ 9 = 3

Answer: 3

Builds on: Spread: standard deviation

Leads to: Combine regions of a normal curve with the 68–95–99.7 rule, Find normal probabilities with z-scores and technology

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Combine regions of a normal curve with the 68–95–99.7 rule

CCSS HSS.ID.A.4England: A-level Statistics

Example

A quantity is normally distributed with mean 21 and standard deviation 9. What percentage of values lie between 3 and 30?

z from −2 to 1
81.5%

Answer: 81.5

Builds on: The normal distribution (68–95–99.7 rule), Calculate and use z-scores

Leads to: Find normal probabilities with z-scores and technology

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Use P(A | B) = P(A and B) ÷ P(B)

CCSS HSS.CP.A.3CCSS HSS.CP.B.6England: A-level Statistics

Example

P(B) = 0.5 and P(A and B) = 0.1. Find P(A | B).

0.1 ÷ 0.5 = 0.2

Answer: 0.2

Builds on: Conditional probability and independence

Leads to: Reverse conditional probability with a tree (tests and filters)

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Reverse conditional probability with a tree (tests and filters)

CCSS HSS.CP.A.3CCSS HSS.CP.B.6England: A-level Statistics

Example

10% of people have a condition. A test is positive for 95% of people who have it and for 10% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.

P(+) = 0.1 × 0.95 + 0.9 × 0.1 = 0.185
0.095 ÷ 0.185 ≈ 0.514

Answer: 0.514

Builds on: Use P(A | B) = P(A and B) ÷ P(B), Tree diagrams and Venn diagrams

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Test for independence using a two-way table

CCSS HSS.CP.A.4CCSS HSS.CP.A.5England: A-level Statistics

Example

Club survey: Plays chess: likes puzzles 18, doesn't 12 No chess: likes puzzles 36, doesn't 24 Are "plays chess" and "likes puzzles" independent?

18/30 = 36/60
Yes

Answer: Yes

Builds on: Conditional probability and independence, Joint and conditional relative frequencies in two-way tables

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