Statistics - Normal distribution

In summary, the individual is having difficulty determining which tables to use for a problem involving percentages and normal distribution. They have encountered discrepancies in their answers when using the normal table versus the percentage points table. They provide a sample problem involving finding the mean and standard deviation for the duration of pregnancy for a certain breed of cow.
  • #1
repugno
78
0
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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  • #2
Can you supply a sample problem?

Doug
 
  • #3
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] days. Only 2.5% of all pregnancies are shorter than 235 days and 15% are longer than 286 days.

Find the value of [tex]\mu[/tex] and [tex]\sigma[/tex]

Any help would be much appreciated, thank you.
 

1. What is a normal distribution?

A normal distribution is a statistical distribution that is often used to represent a large set of data. It is a bell-shaped curve that is symmetrical around the mean, with most of the data falling within one standard deviation of the mean.

2. What are the characteristics of a normal distribution?

The characteristics of a normal distribution include a symmetrical shape, with the mean, median, and mode all being equal. It also follows the 68-95-99.7 rule, where approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

3. How is the normal distribution used in statistics?

The normal distribution is used in statistics to analyze and interpret data. It is often used to determine the probability of a certain outcome occurring, as well as to calculate confidence intervals and perform hypothesis testing. It is also used to compare different data sets and make predictions based on the data.

4. What is the relationship between the normal distribution and 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. This means that for large enough sample sizes, the data will follow a normal distribution regardless of the underlying distribution of the population.

5. How can the normal distribution be applied in real-life scenarios?

The normal distribution can be applied in real-life scenarios to analyze and interpret data, make predictions, and solve problems. For example, it can be used in finance to model stock prices, in medicine to analyze the effectiveness of a treatment, and in quality control to monitor production processes. It is also commonly used in social sciences, such as psychology and sociology, to study human behavior and traits.

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