Statistics and Probability Answers

suppose we have a populationof size N=5 consisting of the abe:6,8,10,12,and 14. take sample of size 2 with out replecment and construct sampling distribution of the sample mean.

9.25: Consider the trash bag case. The mean and the standard deviation of the sample of n = 40 trash bag breaking strengths are _ = 50.575 and s = 1.6438. Test H0 : µ = 50 versus Ha : µ > 50 by setting a equal to .05 and using a critical value rule. Also, interpret the (computer calculated) p-value of .0164 for the test.

The table below gives the results of a matched-pairs study comparing two different foot creams D and E, for treating timea pedis (athlete's foot), with each subject given Cream D on one foot, Cream E on the other foot. Is there sufficient evidence showing one cream better than the other?

Treatment with Cream D
Cured Not Cured
16 17
Treatment with Cream E
Not Cured - 38 14

The marks obtained by a number of students in a certain subject are approximately normally distributed with mean 65 and standard deviation 5. If 3 students are selected at random from this group, what is the probability that at least 1 of them would have scored above 75?

Find the probability that a person tossing 3 fair coins get either all heads or all tails for the second time on the fifth trial.

A public health official claims that the mean home water use is 350 gallons a day. To verify this claim 20 randomly selected homes was studied, with the result that the mean is 353.8 with standard deviation 21.84.

A trucking firm is suspicious of the claim that the average lifetime of certain tires is at least 28000 miles. To check the claim , the firm puts 40 of these tires on its trucks , and gets a mean lifetime of 27463 miles with a standard deviation of 1348 miles . What can it conclude if the probability of a type I error is to be atleast 0.01 ?

For a certain Binary, communication channel, the probability that a transmitted ‘0’ is received as a ‘0’ is 0.95 and the probability that a transmitted ‘1’ is received as ‘1’ is 0.90. If the probability that a ‘0’ is transmitted is
0.4, find the probability that
(i) a ‘1’ was transmitted given that a ‘1’ was received
(ii) a ’1’ is received

A and B alternatively throw a pair of dice. A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6. If A begins, show that his chance of winning is 30/61.

Suppose thatthe joint density of X and Y is given by
(x,y)=e-(x/y).e(-y) ,0<x<∞,0<y<∞ and is o otherwise. Find P(X>1 / Y=y).