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Probability

Normal & Poisson approximation to binomial distribution

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

Normal approximation to binomial distribution

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?

Binomial distribution

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,

Poisson approximation to binomial distribution

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

Probability

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

Probability

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)

Probability

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

Probability

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

Probability

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

Probability

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?

Poisson vs. Gaussian distribution

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.

Probability function

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

Distribution

If there are repeated dependent trial, what distribution should be used? a. binomial b. multinomial c. Poisson d. hypergeometric

Probability

A retail sales worker finds that the probability of making a sale is .23. If she talks to four customer today, what is the probability of her making four sales? a. 0.003 b. 0.03 c. 0.30 d. 0.001

Probability

A shipment of 50 VCRs had 6 defectives. If a person bought two cameras, find the probability of getting 2 defectives. a. .50 b. .10 c. .0122 d. .05

Intro to Statistics Question

A bowl contains 6 red, 4 black, and 3 yellow marbles. How many ways can 2 red, 2 black, and 1 yellow marble be drawn. a. 270 b. 540 c. 625 d. 100

Intro to Statistics Question

If the outcome of one event does not affect the probability of another even, the two events are considered: a. independent b. mutually exclusive c. dependent d. none of the above

Probability

Find the probability of drawing a jack from a ordinary card deck.

Statistics - Probability

1) A record store owner wants to determine consumer tastes. She decides to observe customers in her store on a particular day and record the number of minutes the each spends in the Alternative Music and Rap sections of the store. She came up with the following data: Alternative Music Rap Mean = x = 25 Mean = 20 St

Probability and Expected Value

Find the expected profit in the given question. The Wilhelms Cola Company plans to market a new pineapple-flavored cola this summer. The decision is whether to package the cola in returnable or in no-return bottles. Currently, the state legislature is considering eliminating no-return bottles. Tybo Wilhelms, president of Wilh

Probability of Guessing Correctly

1. A committee consists of five Chicanos, two Asians, three African Americans, and two Caucasions. a) A subcommittee of four is chosen at random. What is the probability that all the ethnic groups are represented on the subcommittee? b) Answer the question for part (a) if a subcommittee of five is chosen. 2. The game of Ma

Probability

There are 5 pairs of shoes with distinct size. Now choose any 4 from it randomly, find the probability that they form at least a pair.

Statistics - polling

1. On February 8, 2002, the Gallup Organization released the results of a poll concerning American attitudes toward the 19th Winter Olympics in Salt Lake City, Utah. The poll results were based on telephone interviews with a randomly selected national sample of 1011 adults, 18 years and older, conducted February 4 - 6, 2002.

Statistics: normally and binomially distributed random variables

1) A videotape store has an average weekly gross of $1,158 with a standard deviation of $120. Assuming this to be a normally distributed random variable, calculate the following: a. Probability the weekly gross will exceed $1,261. b. Proportion of weeks the weekly gross is less than $1,080. c. Probability the weekly gross is