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In: Statistics and Probability

For the following situations. Please indicate a statistical distribution that would be appropriate to model the...

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.

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