Probability (Normal population distribution)

In summary, the conversation is about finding the probability that the sampling mean from one sample of apples is larger than the sampling mean from another sample by a specific range. The person asking for help is unsure about the concept of sampling distribution and is advised to review their notes or textbook for more information before receiving assistance.
  • #1
yyh1
4
0
Can anyone help me to solve this question:

A random sample of twenty-five apples is obtained from a normal population distribution with a mean of 80 grams and a standard deviation of 5 grams. Another random sample of 36 apples is obtained from a population distribution having a mean of 75 grams and a standard deviation of 3 grams. Find the probability that the sampling mean from the first sample is bigger than the sampling mean from the second sample with at least 3.4 grams but less than 5.9 grams.
 
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  • #2
Interesting. What do you know about the sampling distributions of the two means?
 
  • #3
statdad said:
Interesting. What do you know about the sampling distributions of the two means?

Hmm.. no idea.. If u know the answer for this question, kindly explain to me.. thx
 
  • #4
the information you need should be in the material you've learned about normal distributions. look in your notes/text for "sampling distribution" or "central limit theorem" - once you have the sampling distribution information, post again.
 
  • #5
I do not get what do u mean by "sampling distribution information", the question is exactly what I written there..
 
  • #6
I believe the question is as you posed: it refers to the 'sampling mean' in two locations. That is the quantity to which I referred: if you have this problem to solve, you should have seen something that used that term, or central limit theorem, or sampling distribution.
You need to provide some evidence of working on this before you get help.
 

What is a normal population distribution?

A normal population distribution is a statistical term used to describe the distribution of a set of data points that follow a bell-shaped curve. This means that most of the data falls near the middle of the curve, with fewer data points at the extremes.

Why is the normal distribution important?

The normal distribution is important because it allows us to make predictions and draw conclusions about a population based on a sample of data. It also serves as a baseline for many statistical tests and is used in various fields such as economics, psychology, and biology.

How is the normal distribution calculated?

The normal distribution is calculated using the mean and standard deviation of a set of data points. The formula for the normal distribution is (1/σ√2π) * e^(-1/2((x-μ)/σ)^2), where σ is the standard deviation and μ is the mean.

What is the central limit theorem?

The central limit theorem states that when independent random variables are added, their sum tends towards a normal distribution, regardless of the distribution of the individual variables. This makes the normal distribution a useful tool for analyzing data and making predictions.

How is the normal distribution used in hypothesis testing?

In hypothesis testing, the normal distribution is used to calculate critical values and p-values. These values help determine whether a hypothesis is statistically significant or not. The normal distribution is also used to calculate confidence intervals, which help us estimate the range of values where the true population mean may lie.

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