Singapore GCE A-Level · H2 Mathematics

Probability and statistics

54 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 54 questions

$X$ has a binomial distribution with $n = 10$ and $p = \frac{1}{5}$ . Find $Var (X)$ .
$X$ has a binomial distribution with $n = 20$ and $p = \frac{1}{4}$ . Find $Var (X)$ .
$X$ has a binomial distribution with $n = 12$ and $p = \frac{1}{3}$ . Find $Var (X)$ .
$X$ has a binomial distribution with $n = 15$ and $p = \frac{2}{5}$ . Find $Var (X)$ .
$X$ has a binomial distribution with $n = 30$ and $p = \frac{1}{6}$ . Find $Var (X)$ .
$X$ has a binomial distribution with $n = 24$ and $p = \frac{1}{2}$ . Find $Var (X)$ .
A fair coin is tossed 4 times. Find the probability of obtaining exactly 2 heads.
A fair coin is tossed 5 times. Find the probability of obtaining exactly 2 heads.
A fair coin is tossed 6 times. Find the probability of obtaining exactly 3 heads.
A fair coin is tossed 5 times. Find the probability of obtaining exactly 3 heads.
A fair coin is tossed 4 times. Find the probability of obtaining exactly 1 heads.
A fair coin is tossed 6 times. Find the probability of obtaining exactly 2 heads.
$X$ is normally distributed with mean $60$ and standard deviation $5$ . Find the $z$ -value corresponding to $X = 70$ .
$X$ is normally distributed with mean $50$ and standard deviation $2$ . Find the $z$ -value corresponding to $X = 45$ .
$X$ is normally distributed with mean $100$ and standard deviation $4$ . Find the $z$ -value corresponding to $X = 110$ .
$X$ is normally distributed with mean $40$ and standard deviation $8$ . Find the $z$ -value corresponding to $X = 32$ .
$X$ is normally distributed with mean $70$ and standard deviation $10$ . Find the $z$ -value corresponding to $X = 85$ .
$X$ is normally distributed with mean $15$ and standard deviation $3$ . Find the $z$ -value corresponding to $X = 21$ .
$X \sim N (50, 1 0^{2})$ . Given that $Φ (\frac{3}{2}) = 0.9332$ , find $P (X > 65)$ .
$X \sim N (100, 1 5^{2})$ . Given that $Φ (2) = 0.9772$ , find $P (X > 130)$ .
$X \sim N (40, 5^{2})$ . Given that $Φ (2) = 0.9772$ , find $P (X > 50)$ .
$X \sim N (20, 4^{2})$ . Given that $Φ (\frac{3}{2}) = 0.9332$ , find $P (X > 26)$ .
$X \sim N (200, 2 0^{2})$ . Given that $Φ (\frac{3}{2}) = 0.9332$ , find $P (X > 230)$ .
The weights of items have standard deviation $12$ g. What is the standard deviation of the mean weight of a random sample of $9$ items?
The weights of items have standard deviation $20$ g. What is the standard deviation of the mean weight of a random sample of $16$ items?
The weights of items have standard deviation $6$ g. What is the standard deviation of the mean weight of a random sample of $4$ items?
The weights of items have standard deviation $15$ g. What is the standard deviation of the mean weight of a random sample of $25$ items?
The weights of items have standard deviation $30$ g. What is the standard deviation of the mean weight of a random sample of $36$ items?
The weights of items have standard deviation $8$ g. What is the standard deviation of the mean weight of a random sample of $64$ items?
Find an unbiased estimate of the population variance from the sample 2, 4, 6, 8, 10.
Find an unbiased estimate of the population variance from the sample 3, 5, 7, 9, 11, 13.
Find an unbiased estimate of the population variance from the sample 1, 3, 5, 7.
Find an unbiased estimate of the population variance from the sample 10, 12, 14, 16, 18.
Find an unbiased estimate of the population variance from the sample 4, 8, 12, 16, 20.
The regression line of $y$ on $x$ is $y = 2 + 3 x$ . Estimate $y$ when $x = 5$ .
The regression line of $y$ on $x$ is $y = 10 - 2 x$ . Estimate $y$ when $x = 4$ .
The regression line of $y$ on $x$ is $y = 1 + 0.5 x$ . Estimate $y$ when $x = 8$ .
The regression line of $y$ on $x$ is $y = 5 + 4 x$ . Estimate $y$ when $x = 3$ .
The regression line of $y$ on $x$ is $y = - 3 + 2 x$ . Estimate $y$ when $x = 6$ .
A product moment correlation coefficient is $r = 1$ . What does this indicate?
A product moment correlation coefficient is $r = - 1$ . What does this indicate?
A product moment correlation coefficient is $r = 0$ . What does this indicate?
A product moment correlation coefficient is $r = 0.9$ . What does this indicate?
A product moment correlation coefficient is $r = - 0.85$ . What does this indicate?
$P (A) = \frac{2}{5}$ , $P (B) = \frac{1}{2}$ and $P (A \cap B) = \frac{1}{5}$ . Find $P (A ∣ B)$ .
$P (A) = \frac{1}{3}$ , $P (B) = \frac{1}{4}$ and $P (A \cap B) = \frac{1}{12}$ . Find $P (A ∣ B)$ .
$P (A) = \frac{3}{4}$ , $P (B) = \frac{2}{3}$ and $P (A \cap B) = \frac{1}{2}$ . Find $P (A ∣ B)$ .
$P (A) = \frac{1}{2}$ , $P (B) = \frac{1}{5}$ and $P (A \cap B) = \frac{1}{10}$ . Find $P (A ∣ B)$ .
$P (A) = \frac{3}{5}$ , $P (B) = \frac{1}{2}$ and $P (A \cap B) = \frac{1}{4}$ . Find $P (A ∣ B)$ .
$P (A) = \frac{1}{6}$ , $P (B) = \frac{1}{3}$ and $P (A \cap B) = \frac{1}{18}$ . Find $P (A ∣ B)$ .
In how many ways can 4 people be seated around a circular table, if rotations of the same arrangement are not counted as different?
In how many ways can 5 people be seated around a circular table, if rotations of the same arrangement are not counted as different?
In how many ways can 6 people be seated around a circular table, if rotations of the same arrangement are not counted as different?
In how many ways can 7 people be seated around a circular table, if rotations of the same arrangement are not counted as different?

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