On average, a student takes dictation at a speed of 100...

On average, a student takes dictation at a speed of 100 words/minute midway through an advanced court reporting course at the American Institute of Court Reporting. Assuming that the dictation speeds of the students are normally distributed and that the standard deviation is 20 words/minute, what is the probability that a student randomly selected from the course can take dictation at a speed: a. Of more than 120 words/minute? b. Between 80 and 120 words/minute? c. Of less than 80 words/minute?

On average, a student takes dictation at a speed of 100 words/minute midway through an advanced court reporting course at the American Institute of Court Reporting. Assuming that the dictation speeds of the students are normally distributed and that the standard deviation is 20 words/minute, what is the probability that a student randomly selected from the course can take dictation at a speed:
a. Of more than 120 words/minute?
b. Between 80 and 120 words/minute?
c. Of less than 80 words/minute?

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Key Concepts

Normal Distribution

A normal distribution is a symmetric, bell-shaped probability distribution that describes how values of a random variable are distributed. It is characterized by two parameters - the mean, which indicates the center of the distribution, and the standard deviation, which measures the spread of the data.

Mean

The mean is the average value of a dataset or distribution. In the context of a normal distribution, the mean is the point around which the data clusters and determines the center of the bell curve.

Standard Deviation

The standard deviation is a measure of the spread or dispersion of data points around the mean. In a normal distribution, it quantifies how much the data deviate from the mean on average, with larger values indicating a wider spread.

Z-Score

A z-score is a standardized measurement that indicates how many standard deviations an element is from the mean. It is used to convert a normal distribution into a standard normal distribution, facilitating the computation of probabilities.

Cumulative Distribution Function (CDF)

The cumulative distribution function calculates the probability that a random variable from a given distribution will be less than or equal to a specific value. For a normal distribution, the CDF is instrumental in determining probabilities associated with ranges of values.

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