Posted: June 1st, 2021

Mathematical Statistics And Probability essay

Practice 1

A consulting group believes that 70% of the people in a positive county are proud of their nicely being safety. Assuming that that’s true, uncover the probability that in a random sample of 15 people from the county: (a) Exactly 10 are proud of their nicely being safety, and interpret. (b) Not more than 10 are proud of their nicely being safety, and interpret. (c) What is the anticipated number of people out of 15 that are proud of their nicely being safety?

Practice 2

agency that manufactures autos claims that the gasoline mileage for its new line of hybrid autos, on the frequent, is 60 miles per gallon with a standard deviation of 4 miles per gallon. A random sample of 16 autos yielded a suggest of 57 miles per gallon. If the company’s declare is true, what is the probability that the sample suggest is decrease than or equal to 57 miles per gallon? Contact upon the company’s declare regarding the suggest gasoline mileage per gallon of its autos. What assumptions did you make?

Practice three

A random sample of measurement 50 from a particular mannequin of 16-ounce tea packets produced a suggest weight of 15.65 ounces. Assume that the weights of these producers of tea packets are normally distributed with commonplace deviation of zero.59 ounce. Uncover a 95% confidence interval for the true suggest μ.

Practice 4

It is claimed that two of three Individuals say that the possibilities of world peace are critically threatened by the nuclear capabilities of various nations. If in a random sample of 400 Individuals, it is found that solely 252 keep this view, do you suppose the declare is true? Use α = zero.05. State any assumptions you make in fixing this draw back.
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