M4 FINAL EXAM (Fall 2024)

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean of a distribution. It is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

How do you calculate the z-score for a given value?

Back

To calculate the z-score, subtract the mean from the value and then divide by the standard deviation: z = (X - μ) / σ.

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What does a negative z-score indicate?

Back

A negative z-score indicates that the value is below the mean of the distribution.

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What does a positive z-score indicate?

Back

A positive z-score indicates that the value is above the mean of the distribution.

Front

In a normal distribution, what percentage of data falls within one standard deviation of the mean?

Back

Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

Front

What is the mean and standard deviation of the scores in Question 1?

Back

The mean is 80 and the standard deviation is 10.

Front

If a score is 54, what is its z-score in Question 1?

Back

The z-score is -2.6.

Front

What is the mean weight of oranges in the orchard?

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The mean weight of the oranges is 5 oz.

Front

How many oranges are expected to weigh less than 5 oz. from a batch of 800?

Back

400 oranges are expected to weigh less than 5 oz.

Front

What is the logarithmic equation given in Question 4?

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