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Applied Probability and Statistics: Estimations, Confidence Intervals, and Distributions

This assignment applies probability and statistics to estimate, calculate confidence intervals, and interpret distributions.

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    Applied Probability and Statistics: Estimations, Confidence Intervals, and Distributions 1) According to a recent study, 1 in every 10 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty - five women and asked each whether she has been a victim of domestic abuse at some point in her life. Find the probability that more than 22 of the women sampled have not been the victim of domestic abuse. (Hint: Does this satisfy the assumptions of a Binomial experiment? Use the Complement Rule to find the probability.) Here, • There are fixed number of independent trials (number of women) • There are two outcomes of every events (abused or not) • The probability of success (not abused) is fixed in trial to trial So all conditions of Binomial distribution is fulfilled. Thus, X~Binomial(n=25,p=0.9) Required probability = P(X>22) = P(X=23)+P(X=24)+P(X=25) = 0.2659+0.1994+0.0718 = 0.5371 2) A physical fitness association is including the mile run in its secondary - school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds. Here, X~Normal(450,40) Required probability = P(X<358) = 𝑃 ( 𝑍 < 358 − 450 40 ) = P(Z< - 2.3) = 0.0107 3) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 17 recently resold 5 - year - old foreign sedans of the same model. These 17 cars were resold at an average price of $12,610 with a standard

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