Standard normal distribution probability

In summary, the study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group Inc. showed that the calls follow the normal distribution with a mean length of time per call of 4.2 minutes and a standard deviation of 0.60 minutes. Using the standard normal distribution, the probability that the calls lasted between 4.2 and 5 minutes is 0.3413, the probability that the calls lasted more than 5 minutes is 0.1587, the probability that the calls lasted between 5 and 6 minutes is 0.3413, and the probability that the calls lasted between 4 and 6 minutes is 0.6826. Additionally, the minimum length of
  • #1
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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  • #2
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?
 

FAQ: Standard normal distribution probability

What is a standard normal distribution?

A standard normal distribution is a type of probability distribution that follows a specific bell-shaped curve, also known as a Gaussian curve. It is characterized by its mean of 0 and standard deviation of 1.

How is the standard normal distribution different from other types of distributions?

The standard normal distribution is unique because it has a mean of 0 and a standard deviation of 1, which makes it easier to compare and analyze data. Other distributions may have different mean and standard deviation values, resulting in different shapes and characteristics of their curves.

What is the significance of the standard normal distribution in statistics?

The standard normal distribution is used widely in statistics because it simplifies the calculation of probabilities for various data sets. It also allows for easy comparison and analysis of data, making it a useful tool for statistical analysis.

How is the standard normal distribution related to the central limit theorem?

The central limit theorem states that as the sample size increases, the distribution of sample means will approach a normal distribution. The standard normal distribution is considered the "standard" because it is the distribution that sample means tend to approach as the sample size increases.

Can any data set be transformed into a standard normal distribution?

No, not all data sets can be transformed into a standard normal distribution. The data must have a symmetrical bell-shaped curve and follow a specific pattern of frequencies for it to be considered a standard normal distribution.

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