5.54 A survey by Frank N.Magid Associates revealed that 3% of Americans are not connected to the Internet at home. Another researcher randomly selects 70 Americans. a. What is the expected number of these who would not be connected to the Internet at home?
b. What is the probability that eight or more are not connected to the Internet at home? c. What is the probability that between three and six (inclusive) are not connected to the Internet at home?

5.51 An office in Albuquerque has 24 workers including management. Eight of the workers commute to work from the west side of the Rio Grande River.Suppose six of the office workers are randomly selected. a. What is the probability that all six workers commute from the west side of the Rio Grande?

b. What is the probability that none of the workers commute from the west side of the Rio Grande?

c. Which probability from parts (a) and (b) was greatest? Why do you think this is?

d. What is the probability that half of the workers do not commute from the west side of the Rio Grande?

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 64% of the cases. Suppose the 15 cases reported today are representative of all complaints. a-1. How many of the problems would you expect to be resolved today? (Round your answer to 2 decimal places.) Number of Problems a-2. What is the standard deviation? (Round your answer to 4 decimal places.) Standard Deviation b. What is the probability 8 of the problems can be resolved today? (Round your answer to 4 decimal places.) Probability c. What is the probability 8 or 9 of the problems can be resolved today? (Round your answer to 4 decimal places.) Probability d. What is the probability more than 10 of the problems can be resolved today? (Round your answer to 4 decimal places.) Probability

In problems 1 – 5, a binomial experiment is conducted with the given parameters. Compute the probability of X successes in the n independent trials of the experiment.

1.         n = 10, p = 0.4, X = 3

2.         n = 40, p = 0.9, X = 38

3.         n = 8, p = 0.8, X = 3

4.         n = 9, p = 0.2, X < 3

5.         n = 7, p = 0.5, X = > 3

According to American Airlines, its flight 1669 from Newark to Charlotte is on time 90% of the time. Suppose 15 flight are randomly selected and the number of on – time flights is recorded.

            a.         Find the probability that exactly 14 flights are on time.

            b.         Find the probability that at least 14 flights are on time.

            c.          Find the probability that fewer than 14 flights are on time.

            d.         Find the probability that between 12 and 14 flights are on time.

            e.         Find the probability that every flight is on time.

Suppose that you know that Y, the number of cars passing in front of your house/apartment/dorm room every weekday is a Poisson Random Variable. If the average number of cars per week day is 25, use Chebychev's Inequality to *bound* the probability that Y is at most 32 and more than 18. Simplify your answer

The number of times that students go to the movies per year has mean is a normal distribution with a mean of 17 with standard deviation of 8. What is the probability that for a group of 10 students, the mean number of times they go to the movies each year is between 14 and 18 times? (round your answer to the nearest hundredth)

***ANSWER IS NOT .2

Suppose that you roll a die and your score is the number shown on the die. On the other
hand, suppose that your friend rolls five dice and his score is the number of 6’s shown out of five rollings. Compute the probability
(a) that the two scores are equal.
(b) that your friend’s score is strictly smaller than yours.

Part 1 Binomial Distribution [Mark 20%/cancer type, 40% total mark]

Five year survival chance from any cancer depends on many factors like availability of treatment options, expertise of attending medical team and more. Five year survival rate is also an important measure and it is used by medical practitioners to report prognosis to patients and family. We will be analyzing five year survival rate of two types of cancer, very aggressive and very treatable cancer and to have comparative analysis of cancer in Norway.

1. Five year survival rate of breast cancer is 87.7%
2. Five year survival rate of esophageal cancer is 16.5%

(NOTE: due to limitation imposed by our available probability distribution table assume survival rate for breast cancer is 90% and for esophageal cancer is 20%)

To simplify our comparative analysis, we will assume 480 patients were admitted in January 2018. For each type of cancer:

1. Calculate the number of patients that are expected to survive at least 5 years, calculate variance and standard deviation expected for 5 year survival.
2. For a selected 15 patients in each category, calculate probability of at least 7 patients surviving past 5 years, compare your calculated value with estimated number from table in page 329. How accurate is our estimation? Do you prefer estimation or calculation methods?
3. Use the table on page 329 of your textbook to determine survival probability for 0 to 15 patients and complete table below.

4. Draw frequency distribution bar graph for each type of cancer
5. What is the minimum/maximum number of survivors expected for given cancer type at 5 years. [HINT: use mean and 3 standard deviations to report outcome].

Part 2 Normal distribution [Mark 30%]

Daily discharge from phosphate mine is normally distributed with a mean daily discharge of 38 mg/L and a standard deviation of 12 mg/L. What proportion of days will the daily discharge exceed 58 mg/L?

Part 3 Normal approximation of binomial Probability Distribution [Mark 30%]

Airlines and hotels often grant reservation in excess to their available capacity, to minimize loss and maximize profitability due to no shows. Suppose that the records of Air Georgian shows that on average, 10% of their prospective passengers will not show up at departure gates. If Air Georgian sells 215 tickets  and their plane has capacity for 200 passengers.

1. Use binomial probability distribution to calculate, the mean of passengers showing up at the gate out of the 215 reservations made
2. Calculate the standard deviation.
3. Calculate standard z score for 200 passengers showing up at the gates.
4. Using normal probability distribution, determine probability of at least 200 passengers will show up!
5. Determine probability of more than 200 passengers showing up at the gate?
6. Determine probability of all 215 passengers showing up at the gate!

Step 1: Players will spin a spinner with 5 different coloured sections. If the player spins RED they end the game with no prize. If they spin any other colour they continue to step 2.

Step 2: Players will roll two dice. If the sum of the two dice is 7+ then the player moves to step 3. If the player rolls a sum less than 7 then the player is out but will get $1 as a prize.

Step 3: Players will roll a single die and remember the number. They will then roll the die a second time. If they roll a different number then what they rolled the first time they are out. If they roll the same number twice they win the jackpot of $25.

1st: Calculate the theoretical probability for each step of the game

2nd: Create a tree diagram for the entire game

3rd: Figure out the probability for the four branches of the tree (As in the four points the game ends at)