A bottle contains 4 laxative and 5 aspirin tablets. 3 tablets are drawn at random from the

bottle. Find the probability that; a) exactly one, b) at most 1 c) at least 2 are laxative

tablet.

2. Want is the probability of getting at most 2 diamonds in the5 selected without

replacement from a well shuffled deck?

3. A massager has to deliver 10 out of 16 letters to computing department the rest to

statistics department. She mixed up the letters and delivered 10 letters at random to

computing department. What is the probability that, only 6 letters for computing

department actually got there?

4. In a class there are 20 students. 6 are compulsive smokers and they always keep

cigarette in their lockers. One day prefects checked at random on 10 lockers. What is the

probability that they find cigarette in at most 2 lockers?

5. A box holds 8 green, 4 white and 8 red beads. 6 beads are drawn at random without

replacement from the box. What is the probability that 3 red, 2 green and 1 white beads

are drawn?

Over a very long period of time, it has been noted that on Friday's 25% of the customers

at the drive-in window at the bank make deposits. What is the probability that it takes 4

customers at the drive-in window before the first one makes a deposit.

2. It is estimated that 45% of people in Fast-Food restaurants order a diet drink with their

lunch. Find the probability that the fourth person orders a diet drink. Also find the

probability that the first diet drinker of th e day occurs before the 5th person.

3. What is the probability of rolling a sum of seven in fewer than three rolls of a pair of

dice? Hint (The random variable, X, is the number of rolls before a sum of 7.)

4. In New York City at rush hour, the chance that a taxicab passes someone and is

available is 15%. a) How many cabs can you expect to pass you for you to find one that

is free and b) what is the probability that more than 10 cabs pass you before you find

one that is free.

5. An urn contains N white and M black balls. Balls are randomly selected, one at a time,

until a black ball is obtained. If we assume that each selected ball is replaced before the

next one is drawn, what is;

a) the probability that exactly n draws are needed?

b) the probability that at least k draws are needed?

c) the expected value and Variance of the number of balls drawn?

6. In a gambling game a player tosses a coin until a head appears. He then receives $2n ,

where n is the number of tosses.

a) What is the probability that the player receives $8.00 in one play of the game?

b) If the player must pay $5.00 to play, what is the win/loss per game?

7. An oil prospector will drill a succession of holes in a given area to find a productive

well. The probability of success is 0.2.

a) What is the probability that the 3rd hole drilled is the first to yield a productive well?

b) If the prospector can afford to drill at most 10 well, what is the probability that he will

fail to find a productive well?

8. A well-travelled highway has itstraffic lights green for 82% of the time. If a person

travelling the road goes through 8 traffic intersections, complete the chart to find a) the

probability that the first red light occur on the nth traffic light and b) the cumulative

probability that the person will hit the red light on or before the nth traffic light.

9. An oil prospector will drill a succession of holes in a given area to find a productive

well. The probability of success is 0.2.

a) What is the probability that the 3rd hole drilled is the first to yield a productive well?

b) If the prospector can afford to drill at most 10 well, what is the probability that he will

fail to find a productive well?

4. The scores from a state standardized test have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. Use the Empirical Rule to find the following. a) What percentage of students have scores between 70 and 130? b) What percentage of students have scores between 55 and 1157 c) Where would approximately 99.9% of the fall between? Measure of variability 5. Test scores for a statistics class had a mean of 79 with a standard deviation of 4.5. Test scores for a calculus class had a mean of 69 with a standard deviation of 3.7. Suppose a student gets a 81 on the statistics test and a 71 on the calculus test. Which score is higher based on the standard deviation? 6. A student scores 56 on a geography test and 285 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 20. The mathematics test has a mean of 300 and a standard deviation of 10. Which score is lower based on the standard deviation?1. Find the sample standard deviation and variance ($; and 5,). a) 15, 16, 17, 18, 19 b) 4, 5, 6,7,9 2. Find the estimated population standard deviation and variance ($; and 5,). a) 15, 16, 17, 18, 19 b) 4, 5, 6,7,9 Using Empirical Rule 3. A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 460 with a standard deviation of 40 on a standardized test. Assuming a bell-shaped distribution... a) Where would approximately 68% of the scores fall between? b) Approximately 99.7% of the scores fall between fall between what scores? c) What percentage of scores fall between 380 and 540?Horvats be larger or smaller for a 90% Cl, using the same data? nthienza for women fil into its associated 95% CIT 4. Manual Transmission Automobiles In 1980 more than 35% of cars purchased had a manual transmission (i.c. stick shift). By 2007 the proportion had decreased to 7.7. A random sample of college students who owned cars revealed the following: out of 122 cars, 26 had stick shifts. Estimate the proportion of college students who drive sticks with 90% confidence. Source: pollingreport.com 5. Private Schools The proportion of students in private schools is around 1 19%. A random sample of 450 students from a wide geographic area indicated that 55 attended private schools. Estimate the true proportion of students attending private schools with 95% confidence. How does your estimate compare to 11%? Source: National Center for Education Statistics (www.nces.ed.gov). 6. Belief in Haunted Places A random sample of 205 are college students was asked if they believed that places el. could be haunted, and 65 responded yes. Estimate the true proportion of college students who believe in the 7-27(4P) Question 2 Now focus on the statistics by Geographical Region. Consider three categories of geographical regions: Texas (all of Texas, i.e. 70.10% of respondents), the Northeast, and all remaining regions. To obtain an estimate for the average salary in the "all remaining regions" category, calculate a simple arithmetic average salary in all regions in this category. a) We randomly draw individual graduates of the school, identify their region of employment (by the three categories above) and consider the average salary the outcome of this random variable. Describe the probability model for this random variable. (3P) b) What is the expected value for this random variable? (3P) c) What is the standard deviation? (4P) The data provided are in US dollars. $1 US is currently worth approximately $1.3 Con. d) What is the expected value for this random variable in Canadian dollars? (2P) e) What is the standard deviation in Canadian dollars? (2P]