Our psychology department received a new statistics text for review. Prof. Smart in his review provided an interesting table of corrections. Type: Alterations: 20%, Spelling 50%, Spelling and alterations: 10%. Assuming that spelling and alterations are the only possible types of corrections, calculate the probability of spot
1. What are the steps I need to calculate probability of events occurring? 2. Could you apply these steps to the following example: A fair die is tossed, and the up face is observed. If the face is even, you win $5. Otherwise, you lose $5? What is the probability?
When assigning probabilities of two simple events, can we assume that each event is always equally likely to occur and, thus assign .5 to each event? Could you provide an example in your explanation?
Saint Paul's Hospital commissioned an independent study to determine if there was a difference between the quality of care provided by hospital-trained nurses and tertiary-trained nurses. Two hundred nurses were rated as either providing Superior Service (S) or Adequate Service (A). The results are as follows: (See attached file
The manager of an Orange dealership keeps records on customers visiting the store. Records show that 40% of the people visiting the store are female. Thirty-five percent (35%) of the females visiting the store will buy an Orange. The records also point out that 20% of the males visiting the store will buy an Orange. a) What i
Suppose used car salesmen tell the truth 2/5 of the time, and 1/3 of the trees in a forest are oak. If 4 used car salesmen say that a certain tree in the forest is oak, what is the probability that the tree is indeed oak. I have not been able to get the correct answer.
A major hat store chain is having a sale on three nationally known brands, A, B and C. Probabilities that Brand A, Brand B or Brand C will not be big sellers are: 0.30, 0.40, and 0.50, respectively. All three brands are manufactured by three independent companies. Calculate the probability that: a. None of the brands will b
What is meant by subjective probability? Provide a definition and an example.
The Smart Hospital released a study done by a prominent consulting firm. Out of a sample of 500 patients, the study listed the number of deaths by types of illness. Disease: Cancer, Deaths(#): 150 Disease: Heart Failure, Deaths(#): 200 Disease: Liver Ailments, Deaths(#): 100 Disease: Other, Deaths(#): 50 What is the pro
Jessica must finish two courses (much like myself), statistics and economics, in order to complete the requirements for a BA degree. All along she has maintained an 80% average. She has calculated probabilities of scoring in the remaining two courses as follows: Probability of scoring 80 in Statistics= 0.80 Probability of sc
Two events, A and B are equally likely. The chance that either A or B happens on a given trial of an experiment is 0.70, while the chance that they both happen on a given trial is only 0.40. What is the probability that event A happens?
In each month, the proportion of "Prize" bonds that win a prize is 1 in 11000. There is a large number of prizes and all bonds are equally likely to win each prize. Show that, for a given month, the probability that a bondholder with 5000 bonds wins at least one prize is 0.365. For a given month find: 1) The probability taht
A fair coin is tossed 100 times. The event that the number of heads obtained is less than 35 is denoted by A. By using a suitable approximation to the binomial distribution, calculate the probability of A. The event that A occurs more than 3 times when 2000 such coins are each tossed 100 times is denoted by B. By usin
It is known that in a sack of mixed bean seeds, 35% are yellow beans. Use the normal approximation to the binomial distribution to find the probability that in a sample of 400 beans there are a) less than 120 yellow beans b) between 120 and 150 yellow beans (inclusive) c) more than 160 yellow beans
The probability that a patient recovers from a rare blood disease is 0.6. If 100 people are known to have contracted this disease, what is the probability that less than 50 people recovers from this rare blood disease?
A hockey team consists of 11 players. It may be assumed that, on every occasion, the probability of any one of the regular members of the team being unavailable for selection is 0.15, independently of all other members. Calculate, giving three significant figures in your answers, the probability that, on a particular occasion,
In a large town, one person in 80, on the average, has blood of type X. a)If 200 blood donors are taken at random, find an approximation to the probability that they include at least five persons having blood of type X. b)How many donors must be taken at random in order that the probability of including at least one donor
A factory packs bolts in boxes of 500. The probability that a bolt is defective is 0.002. Find the probability that a box contains 2 defective bolts.
1. A random variable X has the following cumulative distribution function F(x) = { 1 - e^(-(x+1)) -1</ x < oo 0 elsewhere. a) 25% of the time, X exceeds what value? b) Find the moment generating function of X, or Mx(t) c) Using your result in (b
Problem: Chances of recieving a direct hit by a scud missile. A scud carries 113kg of explosive, has blast are of 91m in diameter and that missiles are being lobbed into an area 80km long and 48km wide. Assume that missiles fall randomly on this area. a) What is the probability of being in the blast area of a missile? b)
Let X be a random variable which follows Poisson Distribution. Assume that the probability P(X=1)=P(X=2), find P(X=3).
The distribution of blood types for a population are: 40% typeA 9% type B 49% type O 2% type AB Suppose that the blood types are independent and that both the husband and the wife follow this distribution of blood type. a) If the wife has type B, what is the probability that the husband has type B? b) What is the pr
Brain cancer is a rare disease. In any year there are about 3.1 cases per 100000 od population. Suppose a small medical insurance company has 150000 people on its books. How many claims stemming from brain cancer should the company expect in any year? What is the probability of getting more than 6 claims related to brain c
Suppose that X is a random variable which can possibly choose 1,2,3,4 with probability P(X=i)=ci, where c is a constant. Find c
Samples of size 49 are drawn from a population with a mean of 36 and a standard deviation of 15. What is the probability that the sample mean is less than 33?
Radiation: The atoms of a radioactive element are randomly disintegrating and emitting alpha particles. The number of alpha particles emitted per second from these atoms during a 30 second period is recorded as follows. 9.38 8.08 8.36 10.44 9.44 8.05 17.78 7.56 14.17 6.73 9.81 4.79 11.98 9.48 6.32 14.
A standard die has its faces painted different colors. Faces3,4,6 are red, faces 2 and 5 are black and face 1 is white. a) Find the probability that when the die is rolled, a black or even numbered face shows uppermost. a game is played by rolling the die onvce. If any of the red faces show uppermost, the player wins the
Let X and Y have the joint pdf f x,y(X,Y) = 2e^(-(x+y)) , 0<x<y , 0<y Find P(Y<3X)
If there are repeated dependent trial, what distribution should be used? a. binomial b. multinomial c. Poisson d. hypergeometric
At a school, the children miss school 17% of the days. If one classroom has 12 children, what is the probability that no children will be absent on a given day. a. .107 b. .17 c. .201 d. .001