Suppose that a clinical test for a rare disease produces 97% true positives and 95% of true negatives. It is also known that only 0.5% of the general population has the disease. What is the probability that a randomly selected individual with a positive test has the disease?

A group of 11 students' cholesterol levels are tested. Suppose the probability of a student having a healthy cholesterol level is 0.25. What is the probability that exactly seven out of 11 students have healthy cholesterol levels? (Round your answer to three decimal places.)

If a seed is planted, it has a 95% chance of growing into a healthy plant.If 12 seeds are planted, what is the probability that exactly 3 don't grow? Round your answer to three decimal places.

The probability that an electronic circuit board contains dirty particles is 0.01. Considering that the plates are independent, what is the probability that 125 plates will be analyzed until we find the first particle?

A sample of 2500 patients were taken to assess a medical test.  40% of the sample had a positive test, 563 patients have the disease and tested negative, and 235 patients do not have the disease and tested positive. What is the probability someone has a positive test if it is known they do have the disease?  (round your answer to 4 decimal places) What is the probability someone does not have the disease if their test is known to be negative?  (round your answer to 4 decimal places)

Suppose 58% of the children in a school are girls.   If a sample of 425 children is selected, what is the probability that the sample proportion of girls will be greater than 63%? Round your answer to four decimal places.

Suppose that jurors are selected randomly from an adult population. What is the probability that all 12 jurors are white when 67% of the population is white? Round your answer to three decimal places.

You are analysing a factory. Stage 3 of the manufacturing process has a 45% chance of finishing on time. If it does finish on time, the chance of Stage 4 finishing late is 20%. The overall chance of Stage 4 finishing on time is 71.2%. What is the chance that Stage 4 finishes late if Stage 3 finished late? Round your answer to 2 decimal places.

Suppose 59% of the students in a university are baseball players. If a sample of 632 students is selected, what is the probability that the sample proportion of baseball players will be greater than 63%? Round your answer to four decimal places.

A blood test for diabetes gives a positive result with a proportion of 0.22 when an individual has diabetes and a negative result with a proportion of 0.11 when they do not. Approximately a proportion of 0.66 of the population has diabetes. If a randomly chosen citizen tested negative, what is the probability that they actually have diabetes? Round your answer to five decimals.