Statistics - Normal distribution

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SUMMARY

The discussion centers on the confusion surrounding the use of the normal distribution table versus the percentage points table in statistical calculations. The user, Doug, encounters discrepancies in answers when applying these tables to problems involving probabilities expressed as percentages. Specifically, he seeks to determine the mean (\mu) and standard deviation (\sigma) for a normally distributed variable, the duration of pregnancy in a certain breed of cow, given specific percentile information. The consensus emphasizes the necessity of using the correct table based on the context of the problem to achieve accurate results.

PREREQUISITES
  • Understanding of normal distribution concepts
  • Familiarity with statistical tables, specifically normal distribution and percentage points tables
  • Ability to interpret percentile information in statistical problems
  • Basic knowledge of mean (\mu) and standard deviation (\sigma) calculations
NEXT STEPS
  • Study the application of normal distribution tables in statistical analysis
  • Learn how to calculate mean and standard deviation from percentile data
  • Explore sample problems involving normal distribution and their solutions
  • Review the differences between normal tables and percentage points tables in statistics
USEFUL FOR

Students, statisticians, and data analysts who are working with normal distributions and require clarity on the application of statistical tables for accurate data interpretation.

repugno
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Greetings to all,

I have run into some extreme difficulty with this straightforward topic. My problem is that I can’t work out which tables to use. There is the normal table and then the percentage points table. When the question states that the probably under the curve is a percentage I would naturally use the percentage points table. However, this is where the problems arise. My answers are different from the textbooks answers, and then when I recalculate using the normal table my answers are right. Then my understanding changes, so only the normal table gets used even with the percentages. But yet again my answers are wrong, because I had to use the percentage table. Please, anyone, shine some light onto this dilemma. Thank you in advance.
 
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Can you supply a sample problem?

Doug
 
Thanks for the reply Doug. Here is one question which has the probabilities as percentages. For some reason I am not suppose to use the percentage points table. Apart from that the question is straightforward.

The duration of pregnancy of a certian breed of cow is normally distributed with mean \mu and standard deviation \sigma days. Only 2.5% of all pregnancies are shorter than 235 days and 15% are longer than 286 days.

Find the value of \mu and \sigma

Any help would be much appreciated, thank you.
 

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