Statistics and Probability Answers

A package of 6 fuses are tested where the probability an individual fuse is defective is 0.05. (That is, 5% of all fuses manufactured are defective).
(a) What is the probability one fuse will be defective?
(b) What is the probability at least one fuse will be defective?
(c) What is the probability that more than one fuse will be defective, given that at
least one is defective?

Suppose that 3% of computer chips produced by a certain machine are defective. The chips are put into packages of 20 chips for distribution to retailers. What is the probability that a randomly selected package of chips will contain at least 2 defective
chips?

The lifetime of a machine is continuous on the interval (0, 40) with probability density function f, where f(t) is proportional to (t + 10)−2, and t is the lifetime in years.
Calculate the probability that the lifetime of the machine part is less than 10 years.

Hint: Show that f(t) is legitimate and find the proportionality constant

A baseball team has scheduled its opening game for April 1. It is assume that if it snows on April 1, the game is postponed and will be play on the next day that, it does not snow. The team purchased insurance against snow. The policy will pay GHS 1,000 for each day, up to 2 days that the game is postponed. It is determined that the number of consecutive days of snow beginning on April 1, is a Poisson random variable with mean 0.6. What is the standard deviation of the amount that the insurance company will have to pay.

A7. A recent study shows that the annual cost of maintaining a building in Accra averages 200 Cedis with a variance of 260 Cedis. If a tax of 30% is introduced on all items associated with the maintenance of building i.e. everything is made 30% more expensive. Calculate the standard deviation of the annual cost of maintaining a building in Accra

A baseball team has scheduled its opening game for April 1. It is assume that if it snows on April 1, the game is postponed and will be play on the next day that, it does not snow. The team purchased insurance against snow. The policy will pay GHS 1,000 for each day, up to 2 days that the game is postponed. It is determined that the number of consecutive days of snow beginning on April 1, is a Poisson random variable with mean 0.6. What is the standard deviation of the amount that the insurance company will have to pay.

Let X be a continuous r.v with density function
f(x) = ( |x|
10
, for − 2 < x < 4
0, elsewhere
. Calculate the expected value of X.

The lifetime of a machine is continuous on the interval (0, 40) with probability density function f, where f(t) is proportional to (t + 10)−2 , and t is the lifetime in years. Calculate the probability that the lifetime of the machine part is less than 10 years. Hint: Show that f(t) is legitimate and find the proportionality constant.

The standard deviation of the breaking strengths of certain cables produced by a company is given as 240 lbs. After a change was introduced in the process of manufacture of these cables, the breaking strengths of a sample of 8 cables showed a standard deviation of 300 lbs. investigate the significance of the apparent increase in variability, using a significance level of (a) 0.05 and (b)0.01.

the regression equation of x and y is 3y-5x+108=0.if the mean value of y is 44 and the variance of x were 9/16 th of the variance of y .find the mean value of x ang correlation coefficient