Statistics and Probability Answers

Construct a 95% confidence interval for the population mean, μ. Assume the population has a
normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a
standard deviation of 10.2.

Find the equation of the regression line for the given data.

x -5 -3 4 1 -1 -2 0 2 3 -4
y 11 6 -6 -1 3 4 1 -4 -5 8

Given H0: μ => 18 and P = 0.085. Do you reject or fail to reject H0 at the 0.05 level of significance?

If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(A | B) is

If 5 million people voted for a ballot which had a yes or a no answer, what is the probability that the outcome is evenly split 50:50?

Thank you

The time required to assemble a piece of machinery is a random variable having a
normal distribution with mean 11 minutes and variance 9 minutes. Find the
probability that assembly of a piece of this kind will take any where between 9 to
16 minutes

The number of flaws in a fiber optics cable follows a Poisson process with an
average of 0.75 per 100 feet. Find the probability of at least three flaws in 200 feet
cable.

The random variable X has Binomial distribution with mean 4 and variance 2.4.
Find the parameters ‘n’ and ‘p’ and hence calculate the probability P[4 £ X £ 6].

Six bullets of which four are blanks, are randomly inserted into a gun. If three
shots are fired from the gun, find the probability that all three bullets fired will be
blank

(b) A new computer network is being designed. The makers claim that it is not compatible with 96% of the equipment already in use.
i. Set up the appropriate null and alternative hypotheses needed to support this claim.
ii. A sample of 400 equipments is tested, and 390 of these equipments require changes. That is, they are not compatible with the new network. Can H0 be rejected at 98% confidence? Justify.