Statistics and Probability Answers

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?

A10. 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?

(A9). 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?

(A11). 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?

(A20). 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?

(A1). 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.

(A5). 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?

company produces electric bulbs. To estimate the average life of the electric
bulbs, the quality inspector of the company selects 80 bulbs randomly.
She finds that the average life of these bulbs is 50 hours. Find the
population average life of the electric bulbs produced by the company
using 95% confidence limits.

3. Your roommate loves to eat Chinese food for dinner. He estimates that on any given night, there’s a 30% chance he’ll choose to eat Chinese food. Suppose you wanted to calculate the probability that, over the next 7 days, you friend eats Chinese food at least 3 times. Which of the following is the most accurate statement about calculating this probability?

A. Because he doesn’t like to eat Chinese food too much in a short period of time, p is not really the same for each trial and so we cannot use the binomial distribution to calculate the desired probability.

B. Because “success” or “failure” have no real meaning in the context of this problem, we cannot use the binomial distribution to calculate the desired probability.

C. Because we do not know the probabilities of your roommate eating any other types of foods, we cannot use the binomial distribution to calculate the desired probability.

1. Suppose IQ scores are normally distributed with mean 100 and standard deviation 10. Which of the following is false?

A. Roughly 68% of people have IQ scores between 90 and 110.
B. A normal probability plot of IQ scores of a random sample of 1,000 people should show a straight line.
C. An IQ score greater than 130 is highly unlikely, but not impossible.
D. An IQ score of 80 is more unusual than an IQ score of 120.

2. A 2005 survey found that 7% of teenagers (ages 13 to 17) suffer from an extreme fear of spiders (arachnophobia). At a summer camp there are 10 teenagers sleeping in each tent. Assume that these 10 teenagers are independent of each other. What is the probability that at least one of them suffers from arachnophobia?

A. 72%
B.82%
C. 42%
D.62%
E. 52%