Question

In the year 2025 Michael Erken is a leading scientist, she is researching at which Parkinson patients are diagnosed with the disease. Suppose this time is normally distributed with a mean of 80 years old and a standard deviation of 5 years.

1. In a random sample of 9 Parkinson’s patients, what is the probability the sample mean is more than 84 years old? Would you classify this observation as an outlier?
2. What is the probability a random selected Parkinson’s patient was diagnosed with the disease after age 84? Would you classify this person as an outlier?
3. What is the Interquartile (IQR) for the age at which Parkinson’s patient are diagnosed?
4. If you took a random sample from this population and constructed a box and whisker plot, approximately what would be three values on the box?
5. One person’s diagnosis age was 1.78 standard deviation above the mean. At what age was this person diagnose?
6. Using Z > 2 as criteria for an outlier, what is the minimum sample size such that a sample mean of 83 years old would be classified as an outlier?
7. As they develop new techniques with the goals of increasing the age at which Parkinson’s patients are diagnosed. He desires the population mean to be such that in a random sample of 9 patients the probability the sample mean is greater than 86 years old to be at least 0.8 (assumer the population standard deviation is 5) In order to accomplish his goals, the population has to be at least?

Answer 1