Failure of certain component follows the distribution

Assignment Help Basic Statistics

Reference no: EM13985509

1. How large should the size of a random sample be so that we can be 90% certain that the sample mean X will not deviate from the true mean by more than σ/2?

2. Let a fair coin be tossed n times and let Sn be the number of heads that turn up. Show that the fraction of heads, Sn/n, will be near to 1/2 for large n. What can we conclude if the coin is not fair?

3. Suppose that a failure of certain component follows the distribution f(x) = px(1 - p)x for x = 0, 1, and zero, elsewhere. How many components must one test in order that the sample mean X will lie within 0.4 of the true state of nature with probability at least as great as 0.95?

Reference no: EM13985509

Questions Cloud

Calcualting the sampling distribution of the sample mean : 1. Let the population be given by {1, 2, 3}. Let p(x) = 1/3 for x = 1, 2, 3. Take samples of size 3 with replacement. (a) Calculate μ and σ2. (b) Obtain the sampling distribution of the sample mean.

Value of the ?nite population correction factor : What is the probability of each sample in part (a), if each sample of size 2 is equally likely? Find the value of the ?nite population correction factor.

Sampling distribution of the sample mean : Let the population be given by the numbers {-2, -1, 0, 1, 2}. Take all random samples of size 3. (a) Without replacement, obtain the following in each case.

Find the greatest number of shirts : A shirt manufacturer knows that, on the average, 2% of his product will not meet quality speci?cations. Find the greatest number of shirts constituting a lot that will have, with probability 0.95, fewer than ?ve defectives.

Failure of certain component follows the distribution : Suppose that a failure of certain component follows the distribution f(x) = px(1 - p)x for x = 0, 1, and zero, elsewhere. How many components must one test in order that the sample mean X will lie within 0.4 of the true state of nature with probabili..

Probability that the number of cars arriving : Find, using Chebyshev's inequality, a lower bound for the probability that the number of cars arriving at the intersection in 1 hour is between 70 and 130.

Variable with probability density function : Let X be a random variable with probability density function 630x4(1 - x)4, 0 1,f(x) = 0, otherwise.

Test the hypothesis that choice of major : Test the hypothesis that the choice of the major by undergraduate students in this university is independent of their gender. Use α = 0.01.

Opinion on collective bargaining by teachers : The following table gives the opinion on collective bargaining by a random sample of 200 employees of a school system, belonging to a teachers' union.

User Account

All Pages