Statistics and Probability Answers

Jane chooses two people at random for the survey and asks them to complete a questionnaire. Write down two ways in which a survey using a questionnaire can be carried out

A financial analyst has found that policy holders are four times as likely to file two claims as to file four claims . If the number of claims filed has a poisson distribution , what is variance of the number of claims filed?

A ball is drawn at random from a box containing 5 blue balls, 3 green balls, and 2 black balls. Determine the probability that the ball drawn is black.

Tests on the breaking strengths if 10 cables were made and showed a mean strength of 1200 psf and a standard deviation of 100 psf. Estimate the (a) mean and the (b) standard deviation of the population of all the cables being produced by the company.

The recorded measurements of sample of soil cohesion are 90, 106, 97, 88, 102 and 94 KPa respectively. (a) Compute the sample mean cohesion. This is considered as the unbiased and efficient estimate of the population mean. (b) Compute the sample variance. (c) Compute the estimated population variance by multiplying the sample variance by (n/n-1). (d) Compare the sample standard deviation with the estimated population standard deviation.

Two streams, A and B, suspected of being contaminated, were tested for their degree of acidity. Analysis of the 6 water samples taken from stream A showed that the mean acidity level is 7.52 with a standard deviation of 0.024 while the 5 samples taken at Stream B showed an acidity level of 7.49 with a standard deviation of 0.032. Using a 0.05 significance level, determine whether the streams have different acidity levels.

Choose a measure of central tendency and discuss why it would or not be effective “statistical summary” for a given data set .

A tobacco company produces blends of tobacco, with each blend containing various proportions of Turkish, domestic, and other tobaccos. The proportions of Turkish and domestic in a blend are random variables with joint density function (X = Turkish and Y = domestic) f(x,y)={(3x-y)/9, 1<x<3 , 1<y<2, 0, elsewhere a) Find the marginal density functions of X and Y. b) Find the mean and variance of X and Y c) Are X and Y independent?

Two streams, A and B, suspected of being contaminated, were tested for their degree of acidity. Analysis of the 6 water samples taken from stream A showed that the mean acidity level is 7.52 with a standard deviation of 0.024 while the 5 samples taken at Stream B showed an acidity level of 7.49 with a standard deviation of 0.032. Using a 0.05 significance level, determine whether the streams have different acidity levels.

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