Normal Distribution: Percentiles

In summary: Thank you for your question. In summary, the number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1263 chips and a standard deviation of 117 chips. The 26th percentile for the number of chocolate chips in a bag is 271 chips, and the number of chocolate chips in a bag that make up the middle 95% of bags is 1211 chips.
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The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1263 chips and a standard deviation of 117chips.
​(a) Determine the 26th percentile for the number of chocolate chips in a bag.
​(b) Determine the number of chocolate chips in a bag that make up the middle 95​% of bags.

I am just a little stuck on this one. I don't know how to go about entering the information into my scientific calculator. The example that I have to go by simply says use technology but I don't know how. Thanks!
 
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Hello and welcome to MHB! (Wave)

Using a thread title of "probability and statistics" in our forum titled "Basic Probability and Statistics" is not what we consider a useful title. the thread title should describe the problem as stated in our rules:

MHB Rule #4 said:
Show the nature of your question in your thread title. The title of a post should be a brief and accurate description of what your question is about. Since we assume everyone needs help, usually urgently, titles such as ‘Urgent help needed’ etc. are pointless, annoying, ineffective and lazy. You should also avoid using symbols such as ? and ! excessively in a post title for reasons already given. An effectively titled post will get more views than one with a useless title. The thread title should be at least one level more specific than the forum in which you post. For example, do not title a thread in Calculus "Calculus Problem", but "Differentiation of a Function" or "Force on a Tank". Do not use $\LaTeX$ in thread titles, as this strains our server and hinders thread searches.

Now, we certainly don't expect our users to have all rules memorized prior to posting, and so I say this only to bring this policy to your attention. :D

In order to use technology to answer these questions, you need to have access to a function which numerically approximates the area under a normal distribution curve and can return raw data values given an area under the curve.

Does your calculator have such a function, and if so, what does the included documentation say about its use?
 

1. What is a normal distribution?

A normal distribution is a probability distribution that is symmetrical and bell-shaped, with the highest frequency of data points occurring at the mean and progressively fewer data points occurring further away from the mean.

2. What are percentiles in a normal distribution?

Percentiles in a normal distribution represent the percentage of data points that fall below a specific value. For example, the 50th percentile (also known as the median) represents the value at which 50% of the data points fall below and 50% fall above.

3. How are percentiles calculated in a normal distribution?

Percentiles in a normal distribution are calculated using the z-score formula, which converts a data point into a standardized score based on its distance from the mean. The standardized score is then used to determine the percentile using a normal distribution table.

4. What is the significance of the 68-95-99.7 rule in a normal distribution?

The 68-95-99.7 rule, also known as the empirical rule, states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. This rule is helpful in understanding the spread of data in a normal distribution.

5. How is a normal distribution used in statistical analysis?

A normal distribution is commonly used in statistical analysis to make assumptions about a population based on a sample. It is also used to calculate probabilities and determine the likelihood of certain events occurring within a population. Additionally, many statistical tests and models assume a normal distribution of data in order to make accurate predictions and inferences.

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