Statistics and Probability Answers

Suppose that the discrete random variable X counts the number of heads in four tosses of a balanced coin. What is the probability of tossing at least two heads?

Question 2. A dairy farmer accidentally allowed some of his cows to graze in a pasture containing weeds that would contaminate the milk from this herd. The farmer estimates that there’s a 10% chance of a cow grazing on some of the flavorful weeds.

(a) Under these conditions, what is the probability that none of the 12 animals in this herd ate the tasty weeds?

(b) Does the Poisson model give a good estimate of the probability that no animal ate the weed

A sample size 25 is picked up at random from a population which is normally distributed with a mean of 100 and variance of 36. Calculate:-

(a) Pr{ ͞X≤99}

(b) Pr{98≤ ͞X≤100}

A manufacturer of laptops reports that among a shipment of 5000 sent to a local distributor, 1000 are slightly defective. If one purchases 10 of these laptops at random from the distributor, what is the probability that exactly 3 are slightly defective? 

A student organization lists as its members 2 freshmen, 3 sophomores, 5 juniors, and 2 seniors. If a team of 4 is to be selected at random, find the probability that all year levels are represented. 

 A fishbowl contains 3 green balls, 2 blue balls, and 4 red balls. In a random sample of 5 balls, find the probability that both blue balls and at least 1 red ball are selected. 

A group of 10 students is used for an experimental study. The group comprises of 3 students with blood type O, 4 with blood type A, and 3 with blood type B. What is the probability that a random sample of 5 will contain 1 student with blood type O, 2 students with blood type A, and 2 students with blood type B?

It is thought that the proportion of defective items produced by a particular machine is 10%. A random sample of 100 items is inspected and found to contain 15 defective items.

(a) State the sample proportion in this test.

(b) Compute its statistical value

The quality control manager at a light bulb factory needs to extend the mean life of a large shipment of new light bulbs. The manager hopes the new light bulb will increase the mean life by more than 350 hours.

(a) State the null and alternative hypotheses.

(b) Determine the type of tailed test the manager should perform.

(c) Interpret the Type I error in this context.

A faculty student committee is to be selected at random from three students and 4 faculty members. The committee is to consist of two persons. Find the probability that the committee will contain:

a. No student

b. One student

c. Two students