In: Statistics and Probability
For the following situations. Please indicate a statistical
distribution that would be appropriate to model the situation.
Additionally, if there is any information about the parameter
values, include those as well.
i) A pesticide is being tested on groups of plants. 10 experiments
are completed. Within each experiment a plant is sprayed with the
pesticide. After one week, the plant is assessed and categorized as
either dead or alive. Pesticides with similar chemicals have a 95%
survival rate.
ii) An athletic trainer is investigating the average mile time for
high school cross country runners. He looks at the data and
observes that it is approximately bell shaped with an average of 5
minutes and 45 seconds.
iii) An economist is looking at US income data. He would like to
use the Gaussian distribution, but notices the data is heavily
skewed.
iv) A mental health practitioner is examining the amount of time
(in months) that patients stick around in rehabilitation
facilities. They will treat the times as continuous. Literature
says that the average survival time is 0.75 months.
v) An engineer is looking to model the measurement error of a new
instrument. The error looks bell shaped and approximately symmetric
around 0.
vi) A popular game show, ”Deal or No Deal,” has 26 cases (numbered
1 to 26) that contain various amounts from $1 to $1,000,000. The
game starts by the contestant picking one of the cases to hold
onto. We are interested in a contestants initial selection.