(5) What is the probability that a five card hand dealt from a standard deck of cards will include fourcards of the same value? (This kind of hand is called a "four of a kind" in Poker.)

(6) A fair coin is tossed ten times in a row.

(a) What is the probability that "heads" comes up exactly five times?

(b) What is the probability that "heads" come up at least eight times?

(c) What is the probability that "heads" come up at least once?

You flip a coin 8 times. What is the probability of seeing exactly four tails?

128/256

186/256

70/256

4/256

You are the treasurer of Montana Corp. and must decide how to hedge (if at all) future payables of 1 million Japanese yen 90 days from now. Call options are available with a premium of $.0004 per unit and an exercise price of $.01040 per Japanese yen. The forecasted spot rate of the Japanese yen in 90 days is $0.01043 with probability 30%, $0.01042 with probability 25%, $0.01039 with probability 25%, and $0.01038 with probability 20%. What is the probability that the call option will be exercised? What is the estimated dollar cash outflows of currency call hedge? 45%; $10,414 55%; $10,793.5 55%; $10,393.5 45%; $10,814

.8.4. For each of the following phrases write down the probability numberthat you feel is represented by the phrase. After doing so, check youranswers to be sure they are consistent. (For example, is your answerto e less than your answer to j?)

a.“There is a better than even chance that...”b.“A possibility exists that...”c.“...has a high likelihood of occurring.”d.“The probability is very high that...”e.“It is very unlikely that...”f.“There is a slight chance...”g.“The chances are better than even...”h.“There is no probability, no serious probability, that...”i.“...is probable.”j.“...is unlikely.”k.“There is a good chance that...”l.“...is quite unlikely.”m.“...is improbable.”n.“...has a high probability.”

A production manager knows that 8.5% of components produced by a particular manufacturing process have some defect. Eight of these components, whose characteristics can be assumed to be independent of each other were examined. a. Write the distribution function in terms of ? and x. b. What is the probability that none of these components has a defect? c. What is the probability that two of the components have a defect? d. What is the probability that between two and seven components have a defect? e. What is the probability that at most three of the components have a defect? f. What is the probability that at least two of these components have a defect? g. What is the expected defective components and the coefficient of variation?

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n= 69​, find the probability of a sample mean being less than 23.3 if m= 23 and sigma =1.17.

The population mean and standard deviation are given below. Find the indicated probability and determine whether a sample mean in the given range below would be considered unusual. If​ convenient, use technology to find the probability.

For a sample of n =31, find the probability of a sample mean being less than 12,750 or greater than 12753 when μ =12,750 and σ =2.3

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of 1.0 liter and a standard deviation of 0.06 liter. Suppose you select a random sample of 25

bottles.

a. What is the probability that the sample mean will be between 0.99 and1.0 liter​?

b. What is the probability that the sample mean will be below 0.98 liter?

c. What is the probability that the sample mean will be greater than 1.01 ​liters?

d. The probability is 90​% that the sample mean amount of soft drink will be at least how​ much?

e. The probability is 90​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)

Homework 4: Probability and z scores

14. Use the data to answer the following questions
14. Show all work (*round 2 decimals places)

• What is the mean & SD for the distribution of scores?
• What is the corresponding z score for each raw score?
• What is the probability of getting a raw score greater than 4?
• What is the probability of getting a raw score less than 2?
• What is the probability of a raw score between 4 & 6?
• What is the probability of a raw score between 3 & 6?

Variable 2: # of traffic violations
2
5
5
3
2
1
1
6
2
4

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of 2.0 liters and a standard deviation of 0.08 liter. Suppose you select a random sample of 25 bottles. a. What is the probability that the sample mean will be between 1.99 and 2.0 liters​? b. What is the probability that the sample mean will be below 1.98 liters​? c. What is the probability that the sample mean will be greater than 2.01 ​liters? d. The probability is 95​% that the sample mean amount of soft drink will be at least how​ much? e. The probability is 95​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)?

A firehose must be able to shoot water to the top of a building 35 m tall when aimed straight up. Water enters this hose at a steady rate of 0.5 m^3/s and shoots out a round nozzle. A) what is the maximum diameter this nozzle can have? B) if the only nozzle available has a diameter twice as great, what is the highest point the water can reach?