Statistics and Probability Answers

8. 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). What is the probability
that more than one fuse will be defective, given that at least one is defective?

9. An archer shoots arrows at a circular target where the central portion of the target inside is called the bull. The archer hits the bull with probability 1/32. Assume that the archer shoots 96 arrows at the target, and that all shoots are independent. What
is an approximated probability that an archer hit not more than one bull?

10. Emmanuel is given a multiple-choice exam with ten questions and each question with five possible answers. He decided to guess randomly for each question. What is the probability that he will get at least six questions correct?

5. A recent study shows that the annual cost of maintaining a building in Accra averages
$200 with a variance of $260. 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 variance of the annual cost of maintaining a building in Accra.

6. Suppose that an airline accepted 12 reservations for a commuter plane with 10 seats.
They know that 7 reservations went to regular commuters who will show up for sure. The other 5 passengers will show up with a 50% chance, independently of each other.
Find the probability that the flight will be overbooked.

7. 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.

8. Suppose a ball is drawn at random from a box containing three white and three black balls. After a ball is drawn, it is then replaced and another drawn. What is the probability that of the first four balls drawn, exactly two are white?

9. In a bolt manufacturing factory, machines A, B, and C produce 25%, 30% and 45% of the total output, respectively. Of their outputs, 7%, 6% and 4% are defective bolts,
respectively. If a bolt drawn at random from the production is found to be defective,
what is the probability that it was manufactured by machine C?

5.A baseball team has scheduled its opening game for April 5. It is assume that if it snows on April 5, 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 $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 expected cost to the nearest one dollar that
the insurance company will have to pay?

6. The mean number of errors due to a bug occurring in a minute is 0.0001. What is the probability that no error will occur in 20 minutes?

7. Suppose that at a busy traffic junction, the probability p of an individual car having an accident is 0.0001. During a certain part of the day, 100 cars pass through the
junction. What is the probability of two or more cars being involved in an accident within this period?

1. Raymond is a basketball player who takes four independent free throws with 70% probability of getting a basket on each shot. Let X be the number of baskets Raymond
gets. Find the probability that he gets exactly 2 baskets, to 3 decimal places.

2. 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. Find
the proportionality constant that makes the f(t) a probability function.

3. Suppose John throws a die repeatedly until he gets a six. What is the probability that he needs to throw more than 10 times to get a six, to 3 decimal places?

4.A random variable X has Poisson distribution with mean equal to 0.4. What is the probability that the random variable is greater than zero?

the average Mark of candidates in an aptitude test was 128.5 with a standard deviation of 8 points to the three scores extracted from the test are 148 102 and 152 what is the average of the extractor scores that are extreme values

Raymond is a basketball player who takes four independent free throws with 70% probability of getting a basket on each shot. Let X be the number of baskets Raymond gets. Find the probability that he gets exactly 2 baskets, to 3 decimal places.

A discrete random variable has probability mass function, P(X = n) = (1/2)^n. Y=1 when x is even and Y= -1 when x is odd. find the expected value of Y

The average mark of candidates in an aptitude test was 128.5 with a standard deviation of 8.2. Three scores extracted from the test are; 148, 102, 152. What is the average of the extracted scores that are extreme values (outliers)?

There are 20 people in a singing group. The mean age of 12 of the members is 18 years.
The mean age of the remaining 8 is 23 years. What is the mean age of the 20 members of
the singing group?