Standard normal distribution probability

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SUMMARY

The discussion focuses on the analysis of long-distance phone call durations from the Pepsi Bottling Group Inc., which follow a normal distribution with a mean of 4.2 minutes and a standard deviation of 0.60 minutes. Key probabilities are calculated for call durations between specified time intervals, including 4.2 to 5 minutes, more than 5 minutes, and 5 to 6 minutes. Additionally, the director of communications seeks to determine the minimum duration for the longest 4 percent of calls. Standard (z) values corresponding to these durations are essential for accurate probability calculations.

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  • Understanding of normal distribution and its properties
  • Knowledge of z-scores and how to calculate them
  • Familiarity with probability calculations related to continuous distributions
  • Basic statistical analysis skills
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  • Learn how to calculate z-scores for normal distribution
  • Study the use of cumulative distribution functions (CDF) for probability calculations
  • Explore the concept of percentiles in normal distributions
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Statisticians, data analysts, and business analysts who need to analyze call duration data and apply normal distribution principles in their reports and decision-making processes.

trastic
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"A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group Inc. showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes.
a.What is the probability the calls lasted between 4.2 and 5 minutes?
b. What is the probability the calls lasted more than 5 minutes?
c. What is the probability the calls lasted between 5 and 6 minutes? d. What is the probability the calls lasted between 4 and 6 minutes?
e. As part of her report to the president,the director of communications would like to report the minimum
length of the longest (in duration) 4 percent of the calls. What is this time?"
 
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trastic said:
"A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group Inc. showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes.
a.What is the probability the calls lasted between 4.2 and 5 minutes?
b. What is the probability the calls lasted more than 5 minutes?
c. What is the probability the calls lasted between 5 and 6 minutes? d. What is the probability the calls lasted between 4 and 6 minutes?
e. As part of her report to the president,the director of communications would like to report the minimum
length of the longest (in duration) 4 percent of the calls. What is this time?"

Well for starters, since you have been TOLD to use the standard normal distribution, what are the standard (z) values that correspond to values in this distribution of 4.2, 5 and 6?
 

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