The mean duration of television commercials is 75 seconds...

Name: Problem 23, Chapter 1: Mathematical Statistics with Applications
Uploaded: 2021-05-07T18:35:14-08:00
Duration: 3 min 8 s
Channel: Bryan Meares
Description: The mean duration of television commercials is 75 seconds with standard deviation 20 seconds. Assume that the durations are approximately normally distributed to answer the following. a. What percentage of commercials last longer than 95 seconds? b. What percentage of the commercials last between 35 and 115 seconds? c. Would you expect commercial to last longer than 2 minutes? Why or why not?

The mean duration of television commercials is 75 seconds with standard deviation 20 seconds. Assume that the durations are approximately normally distributed to answer the following. a. What percentage of commercials last longer than 95 seconds? b. What percentage of the commercials last between 35 and 115 seconds? c. Would you expect commercial to last longer than 2 minutes? Why or why not?

The mean duration of television commercials is 75 seconds with standard deviation 20 seconds. Assume that the durations are approximately normally distributed to answer the following.
a. What percentage of commercials last longer than 95 seconds?
b. What percentage of the commercials last between 35 and 115 seconds?
c. Would you expect commercial to last longer than 2 minutes? Why or why not?

Key Concepts

Empirical Rule

The Empirical Rule, or the 68-95-99.7 rule, states that in a normal distribution, approximately 68% of data lies within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This rule provides a quick estimate of the spread of data and helps in assessing the likelihood of extreme values or outliers.

Probability Calculation Using Normal Distribution

Calculating probabilities in a normal distribution involves finding the area under the curve corresponding to a range of values. This process is carried out by converting raw scores to z-scores and referencing standard normal tables or computational tools to obtain the cumulative probabilities, which can then be used to answer questions about the likelihood of observations falling within certain ranges.

Normal Distribution

The normal distribution is a continuous probability distribution that is symmetric about its mean. It is characterized by its bell-shaped curve, where the mean, median, and mode coincide. This distribution is widely used in statistics to model naturally occurring phenomena due to its appealing mathematical properties, which simplify probability calculations and statistical inference.

Z-Score

The z-score represents the number of standard deviations a specific observation or data point is from the mean of the distribution. By standardizing data into z-scores, one can compare different data points across different normal distributions and easily determine the probability of observing such values using the standard normal distribution.

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