Statistics and Probability Answers

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?

a recent survey found that 68.6% of the population own their homes, In a random sample of 150 heads of households, 92 responded that they owned their homes. By using alpha = 0.01 does that suggest a difference from the national proportion

Is the following statement sometimes, always or never true? If they are only true give examples or conditions under which they are true and under which they are false.
1. Half of the students taking a test score less than the average mark.

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.

A random variable X has the cumulative distribution function given as
F(x) =



0, for x < 1
x
2
2 2x + 2
2
, for 1 ≤ x < 2
1, for x ≥ 2

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 first four balls drawn, exactly two are white?

A hospital receives 30% of its COVID-19 vaccine shipments from Ghana Health Service
and the remainder of its shipments from neighbouring West African countries. Each
shipment contains a very large number of vaccine vials. For GHS's shipments, 8% of the
vials are inefective and for the neighbouring countries, 3% of the vials are inefective.
The hospital tests 30 randomly selected vials from a shipment and finds that one is
inefective. What is the probability that the shipment came from neighbouring West
African countries?

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 financial analyst has found out that, policyholders are four times as likely to file two
claims as to file four claims. If the number of claims led has a Poisson distribution,
what is the expected value of the number of claims led?

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.