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A large university offers stem (science, technology, engineering, and mathematics) internships to women in stem majors at the university. A woman must be 20 years or older to meet the age requirement for the internships. The table shows the probability distribution of the ages of the women in stem majors at the university.
A large university offers stem (science, technology, engineering, and mathematics) internships to women in stem majors at the university. A woman must be 20 years or older to meet the age requirement for the internships. The table shows the probability distribution of the ages of the women in stem majors at the university.
The correct answers for thislarge universityofferingSTEMare:(A) 0.223(B) 0.0322(C) It is more likely(A) To findthe probabilitythat a woman selected will not meet the age requirement, we add up the probabilities of her being 17, 18, or 19 years old:P(not meeting age requirement) = P(17 years) + P(18 years) + P(19 years)P(not meeting age requirement) = 0.005 + 0.107 + 0.111P(not meeting age requirement) = 0.223(B) To find the probability that at least 30% ofthe womenin the sample will not meet the age requirement, we can use the binomial distribution formula to find the probability that 0, 1, 2, ..., 30 women in the sample will not meet the age requirement, and then subtract this from 1 to get the complement:P(at least 30% not meeting age requirement) = 1 - Σ (from k = 0 to 30) (C(100, k) * 0.223^k * (1 - 0.223)^(100-k))P(at least 30% not meeting age requirement) = 0.0322Where:C(100, k) is the binomial coefficient, representing the number of combinations of 100 women taken k at a time.(C) Tocompare the likelihoodof a woman who does not meet the age requirement being selected in a stratified random sample versus a simple random sample, we need to find the probability of her being selected in each scenario.In the stratified random sample, 30 women are selected from the group of women who do not meet the age requirement, and 70 are selected from the group who do meet the age requirement. So, the probability of a woman who does not meet the age requirement being selected in this scenario is:P(selected in stratified random sample) = 30/100 * (0.005 + 0.107 + 0.111) / (0.005 + 0.107 + 0.111 + 0.252 + 0.249 + 0.213 + 0.063)P(selected in stratified random sample) = 30/100 * 0.223 / (1 - 0.223)In asimple random sample,a woman has a 0.223 probability of being selected if she does not meet the age requirement and a 0.777 probability of being selected if she does meet the age requirement. So, the probability of a woman who does not meet the age requirement being selected in this scenario is:P(selected in simple random sample) = 0.223 / (0.223 + 0.777)P(selected in simple random sample) = 0.223Since theprobability of a womanbeing selected in the stratified random sample is greater than the probability of her being selected in a simple random sample, we can conclude that she ismore likely to be selectedin a stratified random sample.This question should be provided as:A large university offers STEM (science, technology, engineering, and mathematics) internships to women in STEM majors at the university. A woman must be 20 years or older to meet the age requirement for the internships. The table shows the probability distribution of the ages of the women in STEM majors at the university.Age (years): 17, 18, 19, 20, 21, 22, 23 or olderProbability: 0.005, 0.107, 0.111, 0.252, 0.249, 0.213, 0.063The university will select a sample of 100 women in STEM majors to participate in a focus group about the internships.(a) Suppose one woman is...