Statistics and Probability Answers

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.

B1. 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?

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.

Find the value of Z if the normal curve area between 0 and Z (positive) is 0.4332.

Find the area under the standard normal distribution which lies between Z = -0.45 and Z = 0.75?

The mean expenditure per customer at a department store is Birr 85 with standard deviation of Birr 9. If a random sample of 40 customers is taken, what is the probability that the sample average expenditure per customer will be
a) Birr 87 or more
b) Less than Birr 82
c) Between Birr 83 and 85

The average grade/mark of all college students is 70 with standard deviation of 20. If a random sample of 49 students is taken, what is the probability that the sample average grade/mark is
a) At least 65
b) Less than 78
c) Between 65 and 72

In a sample of 1000 workers, if 200 of them are graduates, then what is the sample proportion of graduate workers? In addition, if 650 of them are married, what is the proportion of married workers?

An expert backgammon player is currently competing in two tournaments. He estimates the probability of winning the first tournament as 0.6 and the probability of winning the second tournament as 0.5. If he wins the first tournament, he estimates the probability of winning the second tournament increases to 0.65 because of an increase in confidence. What is the probability of:
(i) the player winning both tournaments?

(ii) the player winning at least one tournament?

•The probability that a student fails the screening test for scoliosis (curvature of the spine) at a local high school is known to be 0.004. Of the next 1875 students who are screened for scoliosis, find the probability that (a) fewer than 5 fail the test.