Estimating the Probability of Earning a Certain Amount in a Weekend as a Waiter

In summary, the Central Limit Theorem is a statistical concept that states that the sampling distribution of the means of multiple samples from a population will approximate a normal distribution, regardless of the underlying distribution of the population. It is important because it allows us to make inferences about a larger population based on a sample, and can be applied to all types of data as long as the sample size is large enough. The minimum sample size needed for the Central Limit Theorem to hold depends on the underlying distribution of the population, and it does not guarantee that the sample mean will be equal to the population mean, but as the sample size increases, the sample mean will become a better estimate of the population mean.
  • #1
h91907
2
0
A waiter believes the distribution of his tips has a model that is slightly skewed to the left, with a mean of $\$8.20$ and a standard deviation of ​$\$5.60$. He usually waits on about 60 parties over a weekend of work. ​a) Estimate the probability that he will earn at least ​$\$600$. ​b) How much does he earn on the best 1​% of such​ weekends?

I worked out A and got 0.0064. I am having an issue on B. I don't understand how you obtain z​.
 
Last edited by a moderator:
Mathematics news on Phys.org
  • #2
I have figured out on my own. 1-00.1= .99 find it on the z-scale!
 

FAQ: Estimating the Probability of Earning a Certain Amount in a Weekend as a Waiter

What is the Central Limit Theorem?

The Central Limit Theorem is a statistical concept that states that regardless of the underlying distribution of a population, the sampling distribution of the means of multiple samples from that population will approximate a normal distribution.

Why is the Central Limit Theorem important?

The Central Limit Theorem is important because it allows us to make inferences about a larger population based on a sample. This is useful in research and data analysis, as it allows us to draw conclusions and make predictions with a certain level of confidence.

Can the Central Limit Theorem be applied to all types of data?

Yes, the Central Limit Theorem can be applied to all types of data, as long as the sample size is large enough. However, it works best for data that is normally distributed.

What is the minimum sample size needed for the Central Limit Theorem to hold?

The minimum sample size needed for the Central Limit Theorem to hold depends on the underlying distribution of the population. In general, a sample size of at least 30 is recommended for the Central Limit Theorem to work effectively.

Does the Central Limit Theorem guarantee that the sample mean will be equal to the population mean?

No, the Central Limit Theorem does not guarantee that the sample mean will be equal to the population mean. However, as the sample size increases, the sample mean will become a better estimate of the population mean.

Similar threads

Limit of probabilities of a large sample
Replies
1
Views
655
B Central Limit Theorem: How does sample size affect the sampling distribution?
Replies
31
Views
749
How can the central limit theorem help us understand the normal distribution?
Replies
13
Views
3K
Central limit theorem and estimates of probability
Replies
10
Views
2K
Central Limit Theorem applied to a Bernoulli distribution
Replies
7
Views
7K
MHB Applying the central limit theorem
Replies
4
Views
3K
I think this is about the Central Limit Theorem
Replies
8
Views
2K
How Does the Central Limit Theorem Apply to Processing Times?
Replies
1
Views
2K
Central limit theorem [probability]
Replies
5
Views
7K
MHB Solving 2 Problems with Exponential RVs: CLT & Probability
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top