Pigmented makeup products like mascara and eye shadow may contain metal​ (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or​ mascara? In a sample of 125 women with cosmetic dermatitis from using eye​ shadow, 11 were diagnosed with a nickel allergy. In a sample of 267 women with cosmetic dermatitis from using​ mascara, 25 were diagnosed with a nickel allergy. Use this information to complete parts a through c below. a. Compute a 95​% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. b. compute a 95% confidence interval for the proportion of women with cosmetic cermatitis from using mascara who have a nickel allergy

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!