The number of hits per day on the Web site of Professional...

The number of hits per day on the Web site of Professional Tool, Inc., is normally distributed with a mean of 700 and a standard deviation of 120 . a. What proportion of days has more than 820 hits per day? b. What proportion of days has between 730 and 820 hits? c. Find the number of hits such that only $5 \%$ of the days will have the number of hits below this number.

The number of hits per day on the Web site of Professional Tool, Inc., is normally distributed with a mean of 700 and a standard deviation of 120 .
a. What proportion of days has more than 820 hits per day?
b. What proportion of days has between 730 and 820 hits?
c. Find the number of hits such that only $5 \%$ of the days will have the number of hits below this number.

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Key Concepts

Normal Distribution

The normal distribution is a continuous probability distribution that is symmetric about its mean, characterized by its bell-shaped curve. It frequently arises in natural and social phenomena due to the Central Limit Theorem, making it a fundamental tool in statistics.

Mean and Standard Deviation

The mean sets the central location of the distribution, while the standard deviation measures the spread or variability around the mean. These parameters define the specific shape and scale of the normal distribution.

Standardization (Z-scores)

Standardization is the process of converting a raw score into a Z-score, which represents the number of standard deviations the raw score is from the mean. This allows comparison across different normal distributions and is essential for calculating probabilities using standard normal tables.

Cumulative Distribution Function (CDF) and Percentiles

The cumulative distribution function (CDF) indicates the probability that a random variable will take a value less than or equal to a given number. Percentiles are cutoff points derived from the CDF, representing the value below which a specific percentage of the data falls. This concept is particularly useful in determining thresholds in a normally distributed dataset.

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