Match each distribution, and explain why, to each of random variable scenarios p

Question

Match each distribution, and explain why, to each of random variable scenarios provided below. A. Binomial Distribution B. Poisson Distribution C. Normal Distribution D. Exponential Distribution E. Uniform Distribution a) The survival time of a plant under certain conditions in days is a continuous random variable with and expected survival time of 16 days. The distribution is positively skewed. b) The chance a part is damaged by a manufacturing process is 0.04. Suppose a sample of 100 parts are tested for damage. Each part is damaged independently of other parts. What type of distribution can be used to model the probability of damaged parts? c) The height of high school aged boys in the US has a distribution that is symmetric, with an average of 68 inches and a standard deviation of 2 inches. d) The number of colds per year of a person taking Vitamin C has a discrete probability distribution with an average of 3 colds. e) The distribution of random numbers produced from a computer is symmetric from 1 to 100 with every number in between have an equal likelihood of occurring. The outcome of the random number generator is a continuous random variable.

Explanation / Answer

a- exponential distribution

Distribution is skewed to right and expected survival time is for 16 days so it is exponential distribution with parameter 1/16.

b- binomial distribution

Here we have 100 independnet trials so binomial distribution with parameter n=100 and p=0.04 will be applied.

c- normal distribution

Since distribution is symmetric so here normal distribution will be applied.

d- Poisson distribution

here poisson distribution with rate parameter 3 will be applied.

e- Uniform distribution

Here uniform distribution over interval [1, 100] will be applied.

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