Finding Probabilities from the Tables (Leaving Cert Mathematics): Quizzes

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Finding Probabilities from the Tables
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What type of probability does the Z-table provide for a given Z-score?

Cumulative probability

What is the formula for calculating a Z-score?

Z=X−μσZ = \frac{X - \mu}{\sigma}

In the Z-score formula, what does μ\mu represent?

The mean

In the Z-score formula, what does σ\sigma represent?

The standard deviation

When locating Z=1.36Z = 1.36 in the Z-table, which row should you find?

1.3

When locating Z=1.36Z = 1.36 in the Z-table, which column should you find?

0.06

What does the cumulative probability from the Z-table represent?

Area under curve to the left

What is the formula for finding P(Z>z)P(Z > z)?

P(Z>z)=1−P(Z≤z)P(Z > z) = 1 - P(Z \leq z)

What is the formula for finding P(a<Z<b)P(a < Z < b)?

P(Z≤b)−P(Z≤a)P(Z \leq b) - P(Z \leq a)

For Z=1.25Z = 1.25, which column should you use in the Z-table?

0.05

If P(Z≤−0.75)=0.2266P(Z \leq -0.75) = 0.2266, what is P(Z>−0.75)P(Z > -0.75)?

0.7734

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

0.7745

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