Solving Problems Using the Normal Distribution (VCE SSCE Mathematical Methods): Quizzes

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Solving Problems Using the Normal Distribution
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What calculator function finds the probability for a normally distributed variable within a range?

Normal CDF

For Normal CDF with no lower bound, what value should be entered?

−∞-\infty or large negative like -99999

If X∼N(55,82)X \sim N(55, 8^2) and Pr(X<50)=0.2660\text{Pr}(X < 50) = 0.2660, what percent complete in under 50 sec?

26.6%

What is the formula for conditional probability Pr(A∣B)\text{Pr}(A|B)?

Pr(A∩B)Pr(B)\frac{\text{Pr}(A \cap B)}{\text{Pr}(B)}

If a<ba < b, what does X<a∩X<bX < a \cap X < b equal?

X<aX < a

Given Pr(X<50)=0.2660\text{Pr}(X<50)=0.2660 and Pr(X<60)=0.7340\text{Pr}(X<60)=0.7340, find Pr(X<50∣X<60)\text{Pr}(X<50|X<60).

0.3624

What formula transforms X∼N(μ,σ2)X \sim N(\mu, \sigma^2) to standard normal ZZ?

Z=X−μσZ = \frac{X - \mu}{\sigma}

If 5% rejected above 2.075 cm and 5% below 1.925 cm (symmetric), what is the mean?

2 cm

For metal rods with μ=2\mu=2 and 2.075−μσ=1.6448\frac{2.075-\mu}{\sigma}=1.6448, find σ\sigma.

0.0456 cm

What common pitfall should be avoided when working with normal distributions?

Confusing variance σ2\sigma^2 with SD σ\sigma

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Continuous Random Variables

Mean and Percentiles for a Continuous Random Variable

Measures of Spread

Properties of Mean and Variance

Cumulative Distribution Functions

The Normal Distribution

Standardisation and the 68–95–99.7% Rule

Determining Normal Probabilities

Solving Problems Using the Normal Distribution

The Normal Approximation to the Binomial Distribution

Show more

Solving Problems Using the Normal Distribution

The Normal Approximation to the Binomial Distribution

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Continuous Random Variables

Mean and Percentiles for a Continuous Random Variable

Measures of Spread

Properties of Mean and Variance

Cumulative Distribution Functions

The Normal Distribution

Standardisation and the 68–95–99.7% Rule

Determining Normal Probabilities

Solving Problems Using the Normal Distribution

The Normal Approximation to the Binomial Distribution

Show more

Solving Problems Using the Normal Distribution

The Normal Approximation to the Binomial Distribution

Explore VCE SSCE Mathematical Methods Flashcards by Topics

Continuous Random Variables

Mean and Percentiles for a Continuous Random Variable

Measures of Spread

Properties of Mean and Variance

Cumulative Distribution Functions

The Normal Distribution

Standardisation and the 68–95–99.7% Rule

Determining Normal Probabilities

Solving Problems Using the Normal Distribution

The Normal Approximation to the Binomial Distribution

Show more

Solving Problems Using the Normal Distribution

The Normal Approximation to the Binomial Distribution

Explore VCE SSCE Mathematical Methods Exam Questions by Topics

Continuous Random Variables

Mean and Percentiles for a Continuous Random Variable

Measures of Spread

Properties of Mean and Variance

Cumulative Distribution Functions

The Normal Distribution

Standardisation and the 68–95–99.7% Rule

Determining Normal Probabilities

Solving Problems Using the Normal Distribution

The Normal Approximation to the Binomial Distribution

Show more

Solving Problems Using the Normal Distribution

The Normal Approximation to the Binomial Distribution

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