10 questions🇬🇧English
🔔 The Normal Distribution – A-level
Maths · A-level — practises normal probabilities, standardising, inverse normal and tests for the mean
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Questions
For any normal distribution X ~ N(μ, σ²), how are the mean, median and mode related?
They are all equal
The median is greater than the mode
The mean is greater than the median
The mode is greater than the mean
20s
A random variable has distribution X ~ N(50, 16). What is its standard deviation?
16
256
4
8
20s
Approximately what percentage of a normal distribution lies within 2 standard deviations of the mean?
99.7%
95%
90%
68%
20s
X ~ N(30, 25). What is the standardised value z for x = 38?
0.625
1.6
8
0.32
30s
X ~ N(100, σ²) and P(X < 120) = 0.9088. What is P(80 < X < 120)?
0.9088
0.1824
0.8176
0.4088
30s
Z ~ N(0, 1). Find the value of a such that P(Z < a) = 0.975:
0.975
2.576
1.645
1.96
30s
X ~ B(100, 0.4) is approximated by a normal distribution. Which normal distribution should be used?
N(24, 40)
N(40, 24)
N(40, 60)
N(40, 40)
30s
X ~ B(n, p) is approximated by Y ~ N(np, np(1 − p)). Which gives the best estimate of P(X ≤ 15)?
P(Y < 15.5)
P(Y < 14.5)
P(Y < 15)
P(Y > 15.5)
30s
X ~ N(μ, 4²) and P(X > 50) = 0.1587. Given that P(Z < 1) = 0.8413, what is μ?
49
54
46
42
60s
X ~ N(μ, 10²). A sample of 25 has mean 83.5. Testing H₀: μ = 80, what is the value of the test statistic z?
0.35
0.875
1.75
8.75
60s