### Normal Approximation to Binomial Distribution

Question : If a fair coin is tossed 200 times, what is the probability that the coin lands tails less than 75 times?

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Question : If a fair coin is tossed 200 times, what is the probability that the coin lands tails less than 75 times?

At a local high school, 1,000 juniors and seniors recently took an aptitude test. The results of the exam were normally distributed with a mean of 250 and a standard deviation of 15. Find a)% of students scoring less than 225 b)number of students that scored less than 180 c)probability of a student selected at random having

Using the joint distribution for two RVs X and Y given by F_XY(x,y) = u(x)u(y)[l-e^(-ax)-e^(-ay)+e^(-a(x+y))] and assuming a = 0.5 in each case, find the probabilities: a) P {X </= 1, y </= 2} B) P {0.5 < X < 1.5} C) P {-1.5 < X </= 2, 1 < Y /= 3}

(1) There are 20 questions in a multiple choice test. Each question has five choices and one correct answer of these five choices. A student did not study. He/she answers the questions at random. What are the probability that he/she makes...more than 10 answers right?exactly eight right?at most 7 right? (2)A can company repor

(Part 1) A random sample of 1000 voters are classified as to whether they are in a low, medium, or high income bracket and whether they favor a new tax reform. The observed frequencies are presented in the table. [see attachment] What is the following probability? P(M'|A) (Part 2) Indications are that the average age at

1.) Dr. Icit is conducting and ESP experiment. A computer is used to randomly select and present a number one of five pictures (house, boat, shoe, people, or horse). The subject must determine which picture is being presented on the computer screen (being viewed only by the researchers). The researcher records the answers as eit

What is the probability that probability that a randomly selected moviegoer attend the romantic comedy? See attached file for full problem description.

Please show all work and some explanation as to why you chose the formula you did. Part 1. In some countries, girls are valued much less than boys. Sometimes women in such countries abort fetuses known to be girls and many girl babies are victims of infanticide. Suppose there are 43 girls to every 57 boys who reach age 1 in

The reported cancer rate for women subjects is 17%, and the reported cancer rate for men subjects is 23%. 220 women and 250 men were selected independently at random. Find the probability that the difference in cancer percentages between men and women will be greater than 5%.

Problems on moment generating functions --------------------------------------- 1. Let X and Y be independent normal rv's, each with mean mu and variance sigma^2. Use moment generating functions to show that X+Y and X-Y are independent normal rv's. 2. If X and Y are independent and M_X(t)=exp{2e^t-2} a

You are manager of bank and you want to make sure customers do not have an overly long wait for a customer representative (other than the ATM or deposit box which requires no employee interaction). You know historically for each customer there is a X% chance a customer will walk in and will need customer service. You are going t

Suppose a coin is flipped and a die is rolled. Let E1 denote the event "the coin shows a tail", let E2 denote the event "the dies shows a 3", and let E3 denote the event "the coin shows heads and the die shows an odd number". Are E1 and E2 mutually exclusive? A family of four children. Assume that it is equally probable

(A roulette wheel has 38 numbers: 18 red, 18 black, a 0, and a 00 (0 and 00 are neither red nor black). When the wheel is spun, all numbers are equally likely to be selected.) What is the probability that the wheel lands on 0? A die is loaded so that the numbers 2 through 6 are equally likely to appear, but 1 is three tim

One fair die is rolled. What is the probability of getting an even number? A card is selected at random from an ordinary 52-card deck. What is the probability that it is a heart? In the Maryland Cash In Hand game, to win the grand prize the contestant must match seven distinct numbers, in any order, among the numbers 1 t

Have to pick 3 out of 7 companies. 2 of the 7 companies will have nuclear difficulties. Please answer: - Chance of not picking a company with nuclear difficulties. - Chance of picking two companies with nuclear difficulties. - Chance of picking one company with nuclear difficulties.

Question : Assuming that X is a binomial random variable with n = 1000 and p = 0.50, find each of the following probabilities. (a) P( X < 500 ) (b) P( 490 < X < 500 ) (c) P( X > 500 ) (d) P( X > 550 )

Question(1): A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. a. Compute the probability that two or fewer will withdraw. b. Compute the probability that exactly four will withdraw. c. Compute the probability that

An auto insurance agency was investigating accident rates for drivers in different age groups. The following contingency provides a joint probability distribution for drivers by age group and accident rate. a) What is the probability that a randomly selected person from the above group has had more than one accident regardle

1. You would like to help some of your math-deficient friends understand probability before they loose too much on lottery tickets. After shuffling two decks of cards, you lay down 40 of them. You say that there should be 10 in each of the four suits: hearts, diamonds, spades, and clubs. What you actually get is 9 hearts, 8 di

1) Type i light bulbs function for a random amount of time having mean mui and standard deviation sigmai, i=1,2. A light bulb randomly chosen from a bin of bulbs is a type 1 bulb with probability p, and type 2 with prob. (1-p). what is the expected value and the variance of the lifetime of this bulb? 2) Mx(t)=exp{2(e^t)-2

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ between 110 and 120 (referred to as bright normal)

Assume that human body temperatures are normally distributed with a mean of 98.20ºF and a standard deviation of 0.62 ºF. a. Bellevue Hopistal in New York uses 100.6ºF as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage

A fair die is rolled twice. Suppose A= The first roll shows an even number B= The second roll shows an odd number C= The two rolls show different numbers Prove or disprove that A,B,C are mutually independent events

On an average, 9 trucks arrive per day at a trucking depot. What is the probability that each day next week, six or more trucks will arrive at the depot?

Three unrelated people go for dinner to a Chinese restaurant which uses MSG in its food. Each person has a 10% probability of developing an adverse reaction to the MSG. Let X be the number of people among the three that do develop an adverse reaction. Find the distribution of X.

The mileage that car owners get from a specific type of radial tire has an exponential distribution. 50% of the car owners get a mileage greater than 30,000 miles. What percentage of the car owners get a mileage greater than 60,000 miles?

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n = 10, x = 2, p = 1/3

A contractor is considering a sale that promises a profit of $31,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $13,000 with a probability of 0.3. What is the expected profit?

The probabilities were obtained by entering the values of n = 6 and p = 0.167. In a clinical test of the drug lipitor, 16.7% of the subjects treated with 10mg experienced headaches. In each case, assume that 6 subjects are randomly selected and treated with 10 mg of atorvastatin, then find the indicated probability. Binomia

1. For a particular group of taxpayers, 25 percent of the returns are audited. Six taxpayers are randomly selected from the group. a. What is the probability two are audited? b. What is the probability two or more are audited? 2. On the average an artist sells two of her works per hour at weekend art shows.