General Normal Distributions (HSC SSCE Mathematics Advanced): Quizzes

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General normal distributions
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What are the mean and standard deviation of the standard normal distribution?

μ=0\mu = 0 and σ=1\sigma = 1

Where are the inflection points for a general normal distribution with mean μ\mu and SD σ\sigma?

At x=μσx = \mu - \sigma and x=μ+σx = \mu + \sigma

What is the total area under a general normal distribution curve?

1

For a normal distribution, how do the mean, median, and mode relate?

They all coincide at x=μx = \mu

If μ=50\mu = 50, σ=10\sigma = 10, and x=65x = 65, what is the z-score?

z=1.5z = 1.5

If μ=100\mu = 100, σ=20\sigma = 20, and z=2z = -2, what is the raw score xx?

x=60x = 60

According to the empirical rule, what % of values lie within two standard deviations of the mean?

Approximately 95%

For normal distribution, approximately what % of values lie within μ±σ\mu \pm \sigma?

Approximately 68%

What is the formula for the first quartile Q1Q_1 in a normal distribution?

Q1=μ0.67σQ_1 = \mu - 0.67\sigma

Using the IQR criterion, values are outliers if outside which range?

μ2.70σ\mu - 2.70\sigma to μ+2.70σ\mu + 2.70\sigma

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