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(Solved by Expert Tutors) 1.For y=a+bx (b>0), show that s?=bs?. (You may assume that y=a+bx.)


2.

You have a data set with 11 observations. Your software calculated the standard deviation as 13. However, your software calculates the standard deviation like we have been doing, except that when we divide by n-1, the software divides by n. Calculate the correct value for s.


3.

X~N(60,2). You are participating in a gamble G: If Xx, you lose $8. x=65. What is E[G]?


4. If {X1,...,Xn} is a random sample from N(135,324), with n = 77, then what is the standard deviation of X??


5.

Your lab is analyzing a certain species of rodent. Prior research indicates that the species? length in feet is normally distributed, with a mean of 1.3 and a standard deviation of 0.22. What is the probability that agiven rodent will be more than 10 inches long? (1 foot = 12 inches).


6. The support from political groups C and D are distributed as C~N(60,25) and D~N(74, 36). 25% of the people are C?s, and 31% are D?s; the remaining persons have an average support of 0, and a standard deviation of 8. What are this region?s overall mean and standard deviation of support? (You may assume that all relevant distributions are independent).


7.

A group of political supporters have support levels distributed as C~N(70,100). 75% o these supporters have a support level that is 70 plus of minus (up to) q points. What is q?


8.?A test was distributed at N(70,100). YOu got a 70. Approximately what percentile does that put you in? (i.e. what percentage of the students did you score higher than?)


9.?For Z~N(0,1), determine Pr[-1


10.?Let U~Unif(0,1). Calculate E[U2]


Please Show Work. There were originally 60 questions and I got stuck on these 10 any descriptive help would be appreciated. :)

 


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