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

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Normal Distribution - Calculations
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In the notation X∼N(30,9)X \sim N(30, 9), what does the second parameter (9) represent?

The variance

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

σ\sigma (standard deviation)

For any normal distribution, what is P(X≥μ)P(X \geq \mu)?

0.50.5

What upper bound value approximates infinity when using Normal CD?

999999999999

Why is P(X≥k)≡P(X>k)P(X \geq k) \equiv P(X > k) for continuous distributions?

Area of strip at x=kx = k is 00

For a normal distribution, what is the relationship between median and mean?

Median = mean

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

0.160.16

If heights have mean 165 cm and SD 3.5 cm, what % are shorter than 160 cm (to 2 d.p.)?

7.66%7.66\%

To find P(16≤X≤18)P(16 \leq X \leq 18), what bounds do you input?

Lower: 16, Upper: 18

If P(168≤X≤174)=0.1906P(168 \leq X \leq 174) = 0.1906 for one woman, what is P(X≥5)P(X \geq 5) for 20 women meeting this criteria?

0.32960.3296

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