Area under Normal Distribution (Leaving Cert Mathematics): Quizzes

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Area under Normal Distribution
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What does the area under the normal distribution curve represent?

Probabilities

What is the mean (μ\mu) of a standard normal distribution?

0

What is the standard deviation (σ\sigma) of a standard normal distribution?

1

What does a Z-score indicate?

How many standard deviations a value is from the mean

Which formula is used to calculate a Z-score?

Z=X−μσZ = \frac{X - \mu}{\sigma}

What does a Z-table provide?

Cumulative area to the left of a Z-score

How do you find the probability between two Z-scores?

Subtract smaller Z-area from larger Z-area

Given μ=100\mu = 100, σ=15\sigma = 15, and X=120X = 120, what is the Z-score?

1.33

If P(Z≤−1)=0.1587P(Z \leq -1) = 0.1587 and P(Z≤1.5)=0.9332P(Z \leq 1.5) = 0.9332, what is P(−1≤Z≤1.5)P(-1 \leq Z \leq 1.5)?

0.7745

What is the total area under the normal distribution curve?

1

What is the shape of a normal distribution?

Bell-shaped and symmetric about the mean

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