CHAPTER 6 STATS PROJECT

Scenario 1: Distributions

• Define: 1.Standard Normal Distribution: a normal probability distribution with a mean of 0 and a standard deviation of 1. The total area under its density curve is equal to 1.
• 2.Uniform Distribution:a continuous random variable has a uniform distribution if it's values are spread evenly over a range of possibilities

dEFINITIONS (CONTINUED)

• 3. Skewed Distribution: a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.

Untitled Slide

Untitled Slide

Untitled Slide

THE CONCEPT OF PROBABILITY

• Standard normal distributions demonstrate the concept of probability as its mean is equal to 0 and it standard deviation is equal to 1. The mean and standard deviation result in an area where standard deviation equals to 1 which demonstrates the concept of probability as the probability will be less than equal to 1.

CONCEPT OF PROBABILITY

• In a uniform distribution, there is a correspondence between area and probability so some probabilities can be found by identifying the corresponding areas.

THE CONCEPT OF Probability

• With a skewed distribution, The mean and the median are to the left or the right of the mode so the probability is likely skewed to the left or the right

EXAMPLES

• An example in which one could determine probability from a standard normal distribution would be trying to find the probability of getting in a car accident.
• An example in which one could determine probability from a uniform distribution would be rolling a die since the probability is constant.

Untitled Slide

• An example in which one could determine probability from a skewed distribution would be finding the probability of finding a used car with a certain mileage.

Scenario 2: Probability Distributions

Untitled Slide

Untitled Slide

Untitled Slide

Untitled Slide

Scenario 3: Binomial Probability Distributions

Find the areas associated with each question in Scenario 2.

• 1. .0062
• 2. 0
• 3. .0055

Untitled Slide

• What Electrical Rating on the final question in Scenario 2 separates the top 1% of meters?
• 148.73 A

Scenario 4: Central Limit Theorem

Untitled Slide

• Explain how we applied the central limit theorem in this chapter.
• We applied the central limit theorem for samples of size n larger than 30 because the approximation gets closer to a normal distribution as the sample size n becomes larger
• We applied the central limit theorem to normal distributions

Untitled Slide

• What adjustment must be made to the z-score under this concept?
• The z-score must be divided by the square root of n or the sample size

QUESTIONS

• 1. In question 1 of Scenario 2, what would be the probability that from a random sample of 250 sheets, that their mean length would be greater than 27.12 cm.
• 0

Untitled Slide

• 2. A company is ordering a shipment of 1,000 resistors from Standard Components. If they need resistors that measure at least 23 ohms, what is the probability that they reject the shipment?
• 1

Untitled Slide

• 3. In a neighborhood of 35 homes, what is the probability that their mean electrical usage will be less than 130 A?
• 2.67 A

CONCLUSION

• This project made me more familiar with different types of normal distributions and how they appear on a graph. Through this project, I also learned how to calculate z scores and find the areas associated with them.
• This project helped me better understand the central limit theorem and the adjustments made to the z score by dividing it by the square root of the sample.