Normal Distribution - Calculations (Edexcel A-Level Mathematics): Quizzes

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Normal Distribution - Calculations
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For X∼N(30,9)X \sim N(30, 9), what is P(X>30)P(X > 30)?

0.50.5

When using Normal CD on a calculator, which parameter should you input?

σ\sigma (standard deviation)

Why is P(X≥k)P(X \geq k) equivalent to P(X>k)P(X > k) for a normal distribution?

Area at single point x=kx = k is 00

What is the relationship between the median and mean in a normal distribution?

Median = mean

For X∼N(20,22)X \sim N(20, 2^2), what is P(X>22)P(X > 22) to 4 d.p.?

0.15870.1587

For X∼N(20,22)X \sim N(20, 2^2), why do P(X>22)P(X > 22) and P(X<18)P(X < 18) have the same value?

Symmetry about mean 2020

What value is used to approximate infinity when setting upper bounds in Normal CD?

999999999999

For heights N(165,3.52)N(165, 3.5^2) cm, what is P(X<160)P(X < 160) to 2 d.p.?

0.080.08

If 2020 women sampled with p=0.1906p = 0.1906, what is P(X≥5)P(X \geq 5) using P(X≤4)=0.6703P(X \leq 4) = 0.6703?

0.32970.3297

In the notation X∼N(μ,σ2)X \sim N(\mu, \sigma^2), what does the second parameter represent?

Variance

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