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# Probability

### Binomial Probability Distribution - Practice Calculations

If your age is an even number, circle: j = 4 If your age is an odd number, circle: j = 3 In problem part A below, j is your number of flights. (my age is 37) Binomial Probability Distribution: P(x) = nCx Ï?**x (1 â?" Ï?)**(n-x) [6-3] Where: · C denotes a combination · n is the number of trials

### Normal probability distributions, proportions, percentages

1. A set of 50 data values has a mean of 44 and a variance of 16. I. Find the standard score (z) for a data value = 51. II. Find the probability of a data value < 51. 2. Find the area under the standard normal curve: I. to the right of z = -1.34 II. to the left of z = -1.34 3. Assume that the population of height

### Finding the Probability of a Box

Given: 2 identical boxes. One contains 10 balls number 1-10 the other 100 balls 1-100. You don't know if the box on the left contains 10 or 100. You flip a coin to choose one of the boxes and ask a friend to pick a ball at random from it. The ball he picks has a number 9 written on it. Find: What is the probability that th

### Decision Analysis

The Lake Placid Town Council has decided to build a new community center to be used for conventions, concerts, and other public events, but considerable controversy surrounds the appropriate size. Many influential citizens want a large center that would be a showcase for the area, but the mayor feels that if demand does not supp

### Probabilities: Airline flight arrivals, owning mutual funds, slow moving product

Problem 5. An airline tracks data on its flight arrivals. Over the past six months, 65 flights on one route arrived early, 273 arrived on time, 218 were late, and 44 were cancelled ? a. What is the probability that a flight is early? On time? Late? Cancelled? ? b. Are these outcomes mutually exclusive? ? c. What is the pr

### Standard Normal Probability Problems

Use the Standard Normal Distribution table to find the indicated area under the standard normal curve. a. Between z = 0 and z = 2.36 b. To the left of z = -1.68 c. Between z = 0.64 and z = 1.52 d. To the right of z = 1.5

### Bernoulli process: On average, 2% make an error on their tax return

Suppose on average 2% make an error on their tax return. Such errors are form a Bernoulli Process. If 100 are audited for errors. a) How many would you expect to make an error out of 100? b) Find the probability that 4 out of 100 made an error. c) Find the probability 3 to 6 out of 100 made an error.

### Probability questions: rule of addition and multiplication, independent events

Please helps with the following problem. 1.) The special rule of addition is used to combine a.) events that total more than one b.) mutually exclusive events c.) events based on subjective probabilities d.) independent events 2) Events are independent if a.) we can count the possible outcomes b.) the pro

### Decision analysis: What is the probability that the person actually has heart disease?

Medical studies have shown that 10 out of 100 adults have heart disease. When a person with heart disease is given an EKG test, a 0.9 probability exists that the test will indicate the presence of heart disease. When a person without heart disease is given an EKG test, a 0.95 probability exists that the test will indicate the pe

### Finding the Probability of Heart Disease

Please help with the following problem. Medical studies have shown that 10 out of 100 adults have heart disease. When a person with heart disease is given an EKG test, a 0.9 probability exists that the test will indicate the presence of heart disease. When a person without heart disease is given an EKG test, a 0.95 probabili

### 14 Statistics Problems

See the attached file for tables and graphs. 4.7 If you roll a die 40 times and 9 of the rolls result in a "5," what empirical probability was observed for the event "5"? 4.10 Webster Aquatic Center offers various levels of swimming lessons year-round. The March 2005 Monday and Wednesday evening lessons included instruc

### Green Elements and Probability Distribution

How many green elements are required to make this a legitimate probability distribution if there are a total of 50 elements in this sample x red blue orange brown green P(x) 0.20 0.18 0.12 0.30

### Discrete Probability Distribution

A company is interested in evaluating its current inspection procedure on shipments of 20 identical items. They take a sample of 5 and accept the shipment if no more than the allowed maximum of the samples are found to be defective. Those that do not pass are directed back to the vendor. What proportion of shipments that have

### Discrete Probability Distribution of Pills

This is a hypergeometric, geometric, negative binomial random variable, or Poisson. A smuggler places 3 narcotic tablets in a bottle of 21 vitamin pills for a total of 24 pills. If U.S. customs tests 2 pills at random what is the probability that at least 1 narcotic pill will be found? The professor gave the answer as 24%,

### Probability / Normal Distribution - Using excel

Please show example by using Excel Assume an examination has a mean of 84.2 and a standard deviation of 10.9 What is the probability of being above 100? What is the probability of being between 77 and 97?

### Probability Distribution Problem

Decide whether the distribution is a probability distribution. If it is not a probability distribution, identify the property that is not satisfied. (References: example 3 and 4 page 197, end of section exercises 25 - 28 page 202 - 203) x P(x) 0 0.49 1 0.05 2 0.32 3 0.07 4 0.02

### Acme Tires Problem

Acme Tires manufactures two types of tires: high performance tires and all weather tires. 31% of the tires they produce are high performance tires. They offer a 40,000 mile warrantee on each of the tires they sell, and 93% of all tires exceed 40,000 miles of tread life. Furthermore, 28% of all the tires sold are both all high pe

### Statistics Using Probability Tables

Assign decimal numbers for probabilities in table below for each x. Don't forget: total for all probabilities should be exactly 1. x = 0 1 2 3 4 ------------------------------------- P(x) = Based on your probability table: 1. Find probability that x is less than 3, P (x < 3) 2. Find pro

### Decision Analysis for Construct Payoff Table

A car needs to decide whether or not to introduce a new car. Profit of 1 million if sales are around 100 million, a profit of 200,000 if sales a around 50 million, or will it lose 2 million if sales are only around 1 million. If the new car is not on market, it will suffer a loss of 400,000. A. Construct a payoff table. B.

### Probability: Coin Problem

I have 5 dimes, 10 pennies, and 8 quarters. I pull out 3 coins, what is the probability that I pull out 3 pennies. I only get to pick three coins. I am looking or the way that one can see this in step by step terms.

### Statistics Analysis of median incomes of families

The following table gives the median incomes of families by level of income and geographical region. East South Midwest West Totals < \$80,000/year 102 98 39 62 301 \$80,

### Binomia Distribution for Republican party: Votes in a Congressional district

The Republican party is interested in studying the number of Republicans that might vote in a particular Congressional district. Assume that the number of voters is binomially distributed by party affiliation (either Republican or not Republican). If ten people show up at the polls, determine the following: Binomial distri

### Multiple Probability Problems

1. In a certain location of downtown Baltimore, it costs \$7 per day to park at parking lots. An illegally parked car, if caught, will be fined \$25, and the chance of being caught is 60%. If money is the only concern of a citizen who must park in this location, should he park at a lot or park illegally? 2. A motorist encounter

### Probability of Pipework Failures

For pipework, 40% of failures are due to operator errors. a) What is the probability that at least 8 of the next 15 errors are due to operator errors? b) What is the probability that no more than 3/10 failures are due to operators? c) Suppose that 5 out of 15 are operator errors. Is it likely that the p=0.4 value tru

### Expected Number of Bulbs

A certain type of lightbulb has an average life of 500 hours with a standard deviation of 100 hours. The length of life of the bulb can be closely approximated by a normal curve. An amusement park buys and installs 10,000 such bulbs. Find the total number that can be expected to last for each period of time.

### Statistics: Talk time on a cell phone and battery life

Talk Time on a Cell Phone: Suppose the 'talk time' in digital mode on a Motorola Timeport P8160 is normally distributed with mean 324 minutes and standard deviation 24 minutes. (a) What percent of the time will a fully charged battery last at least 330 minutes? (b) What is the probability that a random sample of n = 15 batt

### Statistics: Probability of wearing glasses if over 60; waiting times; failure rate on test

Please see the formula sheet and standard normal distribution table to be used. Only use a scientific or graphing calculator (Excel does not help me) and please show all working out. Question 8 A recent study showed that 75% of all people over 60 years of age wear eye glasses. If a random sample of five persons over the

### Statistics: Tree diagram, probability of apples or oranges

** Please see the attached file for the complete problem description ** A box contains nine apples and six oranges. You randomly pick a piece of fruit from the box, and then randomly pick a second piece of fruit from the box without replacing the first piece selected. a. Sketch a tree diagram for this experiment. b. What i

### Statistics: Analyze random sample of 1000 voters for income level to political party

Please find the attached question. Also, please see the formula sheet and standard normal distribution table to be used. Only use a scientific or graphing calculator (Excel does not help me) and please show all working out. Question 5 A random sample of 1000 voters was cross-classified according to income level an