MHB Standard normal distribution probability

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The discussion centers on the analysis of long-distance phone call durations from Pepsi Bottling Group Inc., which follow a normal distribution with a mean of 4.2 minutes and a standard deviation of 0.60 minutes. Participants are tasked with calculating various probabilities related to call durations, including the likelihood of calls lasting between specific time intervals and identifying the minimum duration for the longest 4 percent of calls. The conversation emphasizes the importance of converting call times into standard (z) values for accurate probability assessments. Understanding these probabilities is crucial for the director of communications in preparing a report for the president. The calculations will provide insights into call duration patterns and help inform corporate decision-making.
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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?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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