11th grade statistics and probability

Question 1

Elena scored 86 in maths (mean 67, sd 12) and 76 in science (mean 66, sd 14). Relative to the class, which was the better result?

• A. Maths
• B. Science

Question 2

Heights have mean 165 cm and standard deviation 10 cm. What height has a z-score of −1?

Answer 

Question 3

In how many ways can 1st, 2nd place be awarded among 9 runners?

Answer 

Question 4

Club survey: Plays chess: likes puzzles 16, doesn't 20 No chess: likes puzzles 48, doesn't 60 Are "plays chess" and "likes puzzles" independent?

• A. Yes
• B. No

Question 5

A factory fills 2000 bottles. Volumes are normally distributed with mean 287 ml and standard deviation 43 ml. About how many bottles hold more than 330 ml?

Answer 

Question 6

The probability it rains tomorrow is 0.6. If it rains, the probability the bus is late is 0.5. What is the probability that it rains and the bus is late?

Answer 

Question 7

Find the population standard deviation of 3, 1, 12, 17, 18, 15. Give 2 decimal places.

Answer 

Question 8

A quantity is normally distributed with mean 75 and standard deviation 2. What percentage of values lie between 75 and 81?

Answer 

Question 9

40% of emails are spam. A filter flags 90% of spam emails and 5% of genuine emails. An email is flagged. What is the probability it is spam? Give 3 decimal places.

Answer 

Question 10

A test has mean 56 and standard deviation 6. Find the z-score of a mark of 71.

Answer 

Question 11

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

Answer 

Question 12

Amara has 5 different books to put on a shelf. In how many different orders can they be arranged?

Answer 

Question 13

Phone survey: Android: under 18 13, 18+ 18 iPhone: under 18 38, 18+ 35 A person aged 18+ is chosen at random. Find P(iPhone | 18+) as a fraction in simplest form.

Answer (as a fraction)

Question 14

Scores have mean 71 and standard deviation 6. What is the z-score of 59?

Answer 

Question 15

5% of people have a condition. A test is positive for 95% of people who have it and for 5% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.

Answer 

Question 16

P(B) = 0.25 and P(A and B) = 0.125. Find P(A | B).

Answer