Real-Life Applications of the Normal Distribution
The normal distribution, also known as the Gaussian distribution, finds widespread utility across various fields due to its remarkable properties. From finance to natural phenomena, its applications are diverse and significant. This bell-shaped curve serves as a fundamental model for understanding and predicting outcomes in scenarios ranging from risk assessment in financial markets to analyzing natural phenomena such as human height distribution. Its versatility lies in its ability to approximate a wide range of natural phenomena, making it a cornerstone in statistical analysis and decision-making processes across disciplines.
Questions
- The government has decided that the free-market price of cheese is too low. Farmers complain that the price floor has reduced their total revenue. Is this possible?
- Assume that IQ scores are normally distributed, with a mean #mu# of 100 and standard deviation #sigma# of 15. What is the probability that a randomly selected person has an IQ score greater than 120?
- Assume that IQ scores are normally distributed, with a mean #mu# of 100 and standard deviation #sigma# of 15. What is the probability that a randomly selected person has an IQ score between 105 and 110?
- Assume that IQ scores are normally distributed, with a mean #mu# of 100 and standard deviation #sigma# of 15. What is the IQ score that separates the IQ scores of the lowest 25% from the rest?
- A market research company employs a large number of typists to enter data into a computer. The time it takes for new typists to learn the computer system is known to have a normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes. What is the proportion of new typists who take more than two hours to learn the computer system?
- The distribution of weights of items produced by a manufacturing process can be approximated by a normal distribution with a mean of 90 grams and a standard deviation of 1 gram. Using the empirical rule, what percentage of the items will either weigh less than 88 grams or more than 92 grams?
- Zack takes the SAT and his best friend Nick takes the ACT. Zack’s SAT math score is 680, and Nick’s ACT math score is 27. SAT math scores in the county are normally distributed, with a mean of 500 and a standard deviation of 100. ACT math scores in the county are also normally distributed, with a mean of 18 and a standard deviation of 6. Assuming that both tests measure the same kind of ability, who has scored better?
- The Interquartile Range (IQR) for a set of normally distributed data with mean µ = 80 is 12. What is the approximate value of σ ?
- How does the normal distribution relate to the real world?
- The length of pregnancies varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. What's the probability that the average pregnancy length for 6 randomly chosen women exceeds 270 days?
- Is there is any application of binomial distribution in our practical life?
- You are scooping ice cream as part of your training at an ice cream shop. The weight of the scoop must be 4 ounces with an absolute deviation of .5 ounce. What is the maximum and the minimum amount of ice cream that are acceptable?
- 2 companies, A and B, drill wells in a rural area. Company A charges a flat fee of RM3500 to drill a well regardless of its depth. Company B charges RM1000 plus RM12 per foot to drill a well. ?
- Cynthia decides she is going to purchase a used passenger car. Her grandparents agree to pay for 50% of the passenger car. To get an idea of prices Cynthia looks at listings in a local used automobile publication and on a local internet site?
- Do you think that there is a high correlation between proficiency in mathematics and proficiency in chemistry? Explain why or why not.