11th grade statistics and probability

Question 1

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

Answer 

Question 2

Diego has 3 different books to put on a shelf. In how many different orders can they be arranged?

Answer 

Question 3

A variable is normally distributed with mean 118 and standard deviation 14. About what percentage of values lie between 104 and 132?

Answer 

Question 4

A test has mean 44 and standard deviation 8. Find the z-score of a mark of 28.

Answer 

Question 5

Find the variance of 7, 9, 3, 6, 5 (treat them as the whole population).

Answer 

Question 6

Heights have mean 155 cm and standard deviation 5 cm. What height has a z-score of 2.5?

Answer 

Question 7

Phone survey: Android: under 18 29, 18+ 32 iPhone: under 18 25, 18+ 6 A person aged 18+ is chosen at random. Find P(iPhone | 18+) as a fraction in simplest form.

Answer (as a fraction)

Question 8

A factory fills 200 bottles. Volumes are normally distributed with mean 259 ml and standard deviation 22 ml. About how many bottles hold less than 237 ml?

Answer 

Question 9

In how many ways can a team of 4 be chosen from 10 players (order does not matter)?

Answer 

Question 10

Mei scored 67 in maths (mean 59, sd 10) and 80 in science (mean 72, sd 11). Relative to the class, which was the better result?

• A. Maths
• B. Science

Question 11

The probability it rains tomorrow is 0.6. If it rains, the probability the bus is late is 0.8. What is the probability that it rains and the bus is late?

Answer 

Question 12

1% 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 13

20% of emails are spam. A filter flags 80% 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 14

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

Answer 

Question 15

A quantity is normally distributed with mean 22 and standard deviation 4. What percentage of values lie between 26 and 30?

Answer 

Question 16

Club survey: Plays chess: likes puzzles 90, doesn't 90 No chess: likes puzzles 45, doesn't 45 Are "plays chess" and "likes puzzles" independent?

• A. Yes
• B. No