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# Probability

### Probability and Statistics of Randomly Selected Numbers

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 ( as on the Wechsler test). Find the probability that a randomly selected adult has an IQ between 90 and 110 (referred to as the normal range).

### Probability and Statisics -

Please show all steps using the formula : p1 +p2 + pn = 1 Find the probability distribution of the value x. mean variance and standard derivation. 1. two dice are rolled . x is the sum of numbers on the top faces. 2. five cards are randomly selected from a standard deck. x is the number of aces in the sample. 3.

### Probability distribution, expectation, and variance

One problem attached There are nine tennis balls in a box, of which only 5 have not previously been used. Four of the balls are chosen randomly from the box....Find the probability distribution, Evaluate the expectation, Evaluate the variance

### Probability problem - A bag contains 8 black balls and 6 white balls. Two balls are drawn out at random, one after the other without replacement. calculate the probabilities that (a) The second ball is black (b) The first ball was white, given that the second ball is black.

A bag contains 8 black balls and 6 white balls. Two balls are drawn out at random, one after the other without replacement. calculate the probabilities that (a) The second ball is black (b) The first ball was white, given that the second ball is black.

### Probability National Science Foundation

Please write the probability formula for each one. 1. Twenty five scientists are seeking financial support from the National Science Foundation. Find the number of ways in which the NSF panel can select four of the twenty five submitted proposals ranking them as first second , third , and fourth. 2. A basket contains 6 red

### Expected Profit method to determine optimum bid

1. Gamma construction company has been asked to bid on the construction of 20 lighted tennis courts for State university. Each court will cost \$20,000 in construction costs, and, in addition, there will be a fixed expense of \$10,000 to cover the preparation and submittal of the bid. Gamma is considering five different bid le

### Statistics: Odds and Decisions

# 1 When playing the lottery in your (or a nearby) state, how many possible "different" tickets are there? How many ways are there to win (note that there are often several levels of winning)? What are your odds of winning? # 2 Do you agree or disagree that the lottery is a tax on people who are bad at math? Drawing

### Statistics and probability problems - 1. Roughly speaking, what is an experiment? An event? Give an example of each. ... [See the attached Question File.]

1. Roughly speaking, what is an experiment? An event? Give an example of each. ... [See the attached Question File.]

### Statistics and Probability Problem

An engineer experiments with a sample of 2 vascular plants (V) and 4 nonvascular plants (N). She randomly selects two plants for further experimentation. (a) Find the probability that the first and second plants are (N) with replacement (With replacement means a sampling method to select samples in which items are repl

### Probabilities and Statistics Question

A box of bolts contntains 8 thick bolts, 5 medium bolts, and 3 thin bolts. A box of nuts contains 6 that fit the thick bolts, 4 that fit the medium bolts, and 2 that fit the thin bolt. One bolt and one nut are chosen at random. QUESTION: What is the probability that the nut fits the bolt? (Note: the sample space consists of

### Solving Conditional Probability

Three pieces of paper labeled 2,4, and 6 are placed in a jar. You randomly select a piece of paper from the jar and then randomly draw k cards (without replacement) from a standard deck of 52 cards, where k is the number on the piece of paper you drew. Given that no aces are selected, what is the probability that the number on t

### What is the variance of the binomial distribution of voters supporting a particular referendum?

In a survey, 80% of the voters support a particular referendum. If 20 voters are chosen at random, and X is the number of voters that support this referendum, find the mean and variance of X.

### Calculating Mean and Variance of a Group

A school is sending 11 children to a camp. If 25% of the children in the school are first graders, and the children are selected at random, what is the mean and variance of the number of first graders chosen?

### What is the Probability that Both Are Girls

In a second grade class containing 14 girls and 7 boys, 2 students are selected at random to give out the math papers. What is the probability that both are girls? Which would be the correct answer: (14x14)/(21x21) (14x13)/(21x20) (14x7)/(21x21) (7x7)/(21x21). In a second grade class

### Waiting Line Models

The Sea View Resort uses a multiple-channel queue registration system. If the average service time is 9 minutes, there are three registration clerks, and guests arrive at the rate of one every 6 minutes, find a. Arrival and service rate. b. the probability all three clerks are idle. c. the probability a g

### Conditional probability of random selection

At a certain college, 53% of the students are female, and 21% of the students major in finance. Furthermore, 12% of the students both are female and major in finance. (a) What is the probability that a randomly selected finance major is female? Round your answer to 2 decimal places. (b) What is the probability tha

### 2 problems: (1) What is the probability that both will fail? Neither will fail? One or the other will fail? (2) What is the probability of a fatal accident over a lifetime? Why might a driver be tempted not to use a seat belt "just on this trip"?

Complete the following attachment showing ALL work! 5.62 A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fai

### Probability in titrations

In an acid - base titration an acid or base is gradually added until the solution is neutral. As the resulting solutions are usually colorless pH is measures to monitor the reaction. Suppose the equivalence point is reached after approx 100ml of a base (NaOH) have been added but that replicates are equally likely to indicate fro

### Statistics - Probability Distribution

Statistics - Probability Distribution - [Please see the attached Questions File]

### Operations management problems

Management Science 1. There is a fixed cost of \$50,000 to start a production process. Once the process has begun, the variable cost per unit is \$25. The revenue per unit is projected to be \$45. Find the break-even point. 2. Administrators at a university are planning to offer a summer seminar. It costs \$3000 to reserve

### Inventory management: Safety-stock, Probability of stock-out, Re-order point

Problem #3 Office Max A product with an annual demand of 1000 units has Co = \$25.50 and Ch = \$8. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with µ = 25 and std deviiation= 5. a. Determine the recommended order quantity. b. Determine the reorder point and safe

### What is the probability of this component failing at least once in 100 hours?

A component has a failure rate per hour of 4.5E-3. The failures are governed by the exponential distribution. What is the probability of this component failing at least once in 100 hours? Please explain equation used and steps to solve the problem.

### Probability-If three parts are selected at random from the bin, what is the probability that exactly two are defective?

A bin contains seven parts. The probability that any part in the bin is defective is 3.5E-3. If three parts are selected at random from the bin, what is the probability that exactly two are defective? Please explain equation used and steps to solve the problem.

### Probability-failure rate

A fire detection sensor is tested for its failure rate and found to have a mean failure rate of 3.6E-2 per hour of exposure with a standard deviation of .4E-2 per hour. The distribution of the failure rates is normal. If a sensor is selected at random from a large lot for installation in a system, what is the probability that it

### Probability-A component has a failure rate per hour of 4.5E-3. The failures are governed by the exponential distribution. What is the probability of this component failing exactly once in 100 hours?

A component has a failure rate per hour of 4.5E-3. The failures are governed by the exponential distribution. What is the probability of this component failing exactly once in 100 hours? Please explain equation used and steps to solve the problem.

### Probability

A bin contains seven parts. The probability that any part in the bin is defective is 3.5E-3. If one part is selected at random from the bin, what is the probability that it is defective? Please explain equation used and steps to solve the problem.

### Using the given probabilities of certain individual events, find the probability of each of the specified combinations of those events.

Using the given probabilities of individual events, find the probabilities that the specified combinations of those events will occur: 1. If the school cafeteria serves meat loaf, there is a 70% chance that they will serve peas. If they do not serve meat loaf, there is a 30% chance that they will serve peas anyway. The stud

### 7 multiple choice questions on probability, probability distribution, normal distribution, Poisson distribution,

1) A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from this program to be interviewed about the introduction of a new fast food outlet on ground floor of the campus building, what is the probability that all four students selected are undergraduate students. A)

### Normal distribution

1) A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Wha

### The probability that a new advertising campaign will increase sales is assessed as being 0.80.

1) The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that cost is kept within budget and the campaign sa