4. The probability that a patient recover from a delicate heart operation is 0.9. What is the probability that exactly 5 of the next 7 patients having this operation survive? Of the next 100 patients having this operation, what is the probability that (a) between 84 and 95 indusive survive? (b)fewer than to survive? 5. A co is tossed 400 times. Use the normal curve approximation to find the probability of obtaining (a) between 105 210 heads inclus (b) exactly 205 heads I fewer than 176 or more 227 heads

a A box in a certain supply room contains seven 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs. Suppose that three bulbs are randomly selected. a. What is the probability that exactly two of the selected bulbs are rated 75-watt? b. What is the probability that all three of the selected bulbs have the same rating? c. What is the probability that one bulb of each type is selected? d. What is the probability that at least two of the selected bulbs are rated 75-watt?

What is the probability that in a group of three people at least two will have the same birth month? (Assume that all sequences of three birth months are equally likely.) (b) What is the probability that in a group of n people, n ≤ 12 , at least two will have the same birth month? (c) What is the probability that in a group of n people, n > 12 , at least two will have the same birth month? (d) What is the probability that at least two members of the U.S. House of Representatives have the same birth date?

Giving a test to a group of students, the grades and gender identities are summarized below

If one student is chosen at random,

Find the probability that the student got an A:   

Find the probability that the student identifies as female AND got a "C": 534​  

Find the probability that the student identifies as female OR got an "C":   

If one student is chosen at random, find the probability that the student identifies as male GIVEN they got a 'B':   

A certain variety of flower seed is sold in packets containing 1000 seeds. It is claimed on the packet that 40% will bloom white and 60% will not bloom red. This may be assumed accurate. 200 seeds are planted for experimental purposes.

Find the probability that half of our experimental plants will bloom white.

Find the probability that between 60 and 90 inclusively will bloom white

Find the probability that exactly 125 will bloom red.

Find the probability that more than the percentage that bloomed white will bloom red in the 200 experimental seed plantation

This is the full question

1. Consider a‘‘duel’’ between two players. Let’s call these players H and D.Now,we have historical information on each because this is not their first duel. H will kill at long range with probability 0.3 and at short range with probability 0.8. D will kill at long range with probability 0.4 and at short range with probability 0.6. Let’s consider a system that awards 10 points for a kill for each player. Build a payoff matrix by computing the expected values as the payoff for each player. Solve the game.

A statistical program is recommended.

Suppose that the magnitude of earthquakes recorded in a region of North America can be modeled as having a gamma distribution with α = 0.8 and β = 2.6.

(b) What is the probability that the magnitude of an earthquake striking the region will exceed 5 on the Richter scale? (Round your answer to four decimal places.)

(c) Using an exponential distribution with mean 2.6 to model the magnitude of an earthquake striking the region, the probability an earthquake will exceed a magnitude of 5 is 0.1462. Is this probability larger or smaller than the probability found in (b)? Explain.

An airliner carries 250 passengers and has doors with a height of 75 in. Heights of men are normally distributed with a mean of 69.0

in and a standard deviation of 2.8 in. Complete parts​ (a) through​ (d).

a. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending.

The probability is 0.9838

​(Round to four decimal places as​ needed.)

b. If half of the 250 passengers are​ men, find the probability that the mean height of the 125 men is less than 75 in.

The probability is nothing.

​(Round to four decimal places as​ needed.)

1. Your company purchases an expensive component from a supplier. You know that the population of the components is normally distributed with a mean ( μ) of 60 months and a standard deviation (σ) of 2 months. Using this information determine:

1. the probability of a component lasting longer than 68 months.
2. the probability of a component lasting less than 63 months.
3. the probability that a component will last between 58 and 65 months.

2. Using the information in the problem above, what is the probability that a sample average (X) from a sample of 25 components will be between 58.5 and 59.6 months?

Your flight has been delayed: At Denver International Airport, 84% of recent flights have arrived on time. A sample of 14 flights is studied. Round the probabilities to four decimal places.

(a) Find the probability that all

14 of the flights were on time

(b) Find the probability that exactly

12 of the flights were on time.

(c) Find the probability that

12 or more of the flights were on time.

(d) Would it be unusual for

13 or more of the flights to be on time?

It would/would not be unusual for 13 or more flights to be on time since the probability is ________