(See attached file for full problem description)
1. The Trail Making Test (TMT) is frequently used in neuropsychological assessment to provide a quick estimate of brain damage in humans. To investigate the neuropsychological deficits in alcoholics, 50 problem drinkers (25 drinkers under the age of 40 and 25 drinkers 40 years or older) were given the TMT and their performance scores observed (the higher the score, the more extensive the brain damage).
Alcoholics < 40 Alcoholics >= 40
Mean Performance Score 39.6 49.7
Standard Deviation 19.7 19.1
a. Using the 68 - 95 - 99.7 Rule (normal distribution), estimate the proportion of alcoholics under age 40 who score between 19.9 and 59.3 on the TMT. (Note: There was a typo on the original version of the test!)
b. Again, using the 68 - 95 - 99.7 Rule, estimate the proportion of alcoholics age 40 and over who score between 11.5 and 87.9 on the TMT.
2. A nearby metropolitan airport commission is considering the establishment of limitations on the extent of noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 6 decibels.
a. What is the probability that a randomly selected jet will generate a noise level greater than 108 decibels in this neighborhood?
b. Suppose a regulation is passed that requires jet noises in this neighborhood to be lower than 105 decibels 95% of the time. Assuming the standard deviation of the noise distribution remains the same, how much will the mean noise level have to be lowered to comply with the regulation?
Two problems solved using hypothesis tests and normal distributions.