11th grade statistics and probability

Question 1

A variable is normally distributed with mean 135 and standard deviation 4. About what percentage of values lie between 131 and 139?

Answer 

Question 2

In how many ways can a team of 3 be chosen from 7 players (order does not matter)?

Answer 

Question 3

P(B) = 0.5 and P(A and B) = 0.25. Find P(A | B).

Answer 

Question 4

Noah scored 72 in maths (mean 61, sd 7) and 82 in science (mean 63, sd 11). Relative to the class, which was the better result?

• A. Maths
• B. Science

Question 5

The probability it rains tomorrow is 0.4. 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 6

Club survey: Plays chess: likes puzzles 39, doesn't 54 No chess: likes puzzles 36, doesn't 57 Are "plays chess" and "likes puzzles" independent?

• A. Yes
• B. No

Question 7

Heights have mean 172 cm and standard deviation 8 cm. What height has a z-score of 2.5?

Answer 

Question 8

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

Answer 

Question 9

40% 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 10

Find the population standard deviation of 19, 14, 9, 11, 7, 17. Give 2 decimal places.

Answer 

Question 11

Scores have mean 59 and standard deviation 6. What is the z-score of 62?

Answer 

Question 12

Phone survey: Android: under 18 10, 18+ 30 iPhone: under 18 37, 18+ 33 A person aged 18+ is chosen at random. Find P(iPhone | 18+) as a fraction in simplest form.

Answer (as a fraction)

Question 13

A factory fills 800 bottles. Volumes are normally distributed with mean 188 ml and standard deviation 35 ml. About how many bottles hold less than 153 ml?

Answer 

Question 14

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

Answer 

Question 15

A test has mean 54 and standard deviation 8. Find the z-score of a mark of 42.

Answer 

Question 16

10% of people have a condition. A test is positive for 99% 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.

Answer