A-Level UK (AQA, Edexcel, OCR) · Mathematics

Statistics and probability

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Treating the eight values $2, 4, 4, 4, 5, 5, 7, 9$ as a whole population, what is the standard deviation?
$X \sim B (10, 0.3)$ . Find $P (X = 2)$ to 4 decimal places.
$X \sim B (8, 0.5)$ . Find $P (X \geq 7)$ to 4 decimal places.
$X \sim B (40, 0.25)$ . What is $Var (X)$ ?
$X \sim N (50, 16)$ (variance 16). Find $P (X > 58)$ .
$X \sim N (100, 1 5^{2})$ . Find the value $k$ such that $P (X < k) = 0.9$ .
$P (A) = 0.5$ , $P (B) = 0.4$ and $P (A \cap B) = 0.2$ . Find $P (A ∣ B)$ .
$P (A) = 0.6$ , $P (B) = 0.5$ and $P (A \cup B) = 0.9$ . Find $P (A \cap B)$ .
A coin is tossed 12 times and lands heads 10 times. Test, using $H_{0} : p = 0.5$ and $H_{1} : p > 0.5$ , and find the p-value to 3 decimal places.
In a hypothesis test, what is the critical region?
A product moment correlation coefficient of $- 0.9$ is found for a sample. What does this suggest?
A regression line $y = 3.2 + 1.5 x$ was fitted to data with $x$ between 5 and 20. Why is using it to predict $y$ when $x = 50$ unreliable?
A school has 600 pupils in Year 12 and 400 in Year 13. A stratified sample of 50 pupils is needed. How many come from each year?
The quartiles of a data set are $Q_{1} = 20$ and $Q_{3} = 32$ . Using the rule that outliers lie more than $1.5 \times IQR$ beyond a quartile, what is the upper boundary?
In a histogram, the class $20 \leq x < 30$ has frequency density $4$ . What is the frequency of that class?
A discrete random variable has $P (X = x) = k x$ for $x = 1, 2, 3, 4$ . Find $E (X)$ .
$X \sim N (25, σ^{2})$ and $P (X < 20) = 0.1587$ . Find $σ$ .
A bag has 5 red and 3 blue counters. Two are drawn without replacement. Find $P (both red)$ .
A bag has 5 red and 3 blue counters. Two are drawn with replacement. Find $P (exactly one red)$ .
Which pair of summary statistics is least affected by a single extreme outlier?

Statistics and probability

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