Hi everybody,

i would first like to apologise, in case i am posting this under the wrong section, as i am a new member. I am in need of help of some stats questions, please help me by providing answers and if possible, some explanation to it.

Thank you all!

4. A financial planner gets a bonus every 3 months based on the following criteria. She will get a bonus of $1000 if she recruits a new client every month. She will get a bonus of $500 if she manages to recruit 2 new clients out of the three months. Otherwise there will be no bonus. Suppose that, for each single month, she will either be able to recruit a new client with a probability of 0.4 or none with a probability of 0.6. Let X be the amount of bonus money she will receive. Find the probability

distribution of X assuming the results for different months are independent.

Determine the expected value of X and its variance.

5. Two investments, X and Y, have the following characteristics:

E(X)=$50, E(Y)=$100,

Compute the variance of the following:

(a) 0.1 X +0.9 Y

(b) 0.4 X + 0.6 Y

© 0.9X + 0.1 Y

Comment on your results obtained

6. A surprise quiz contains 4 multiple-choice questions: Question 1 has 5 suggested answers, Question 2 has 4, question 3 has 3 and Question 3 has two. A completely unprepared student decides to choose the answers at random. Let X denote the number of questions the student answers correctly. Determine the probability distribution of X.

7. The automatic opening device of a military cargo parachute has been designed to

open when the parachute is 200 m above the ground. Suppose opening altitude

actually has a normal distribution with mean value 200 m and standard deviation

40 m. Equipment damage will occur if the parachute opens at an altitude 100 m.

What is the probability that there is equipment damage to the payload of at least

one of five independent dropped parachutes?

8. The number of requests for assistance received by a towing service is a Poisson

process with rate =4 per hour.

a) What is the probability that exactly 10 requests are received during a particular

2-hour period?

b) If the operators of the towing service took a 30-minute break for lunch, what

is the probability that they do not miss any calls for assistance?

c) How many calls would you expect during their break?

9. A busy restaurant determined that between 6.30 pm and 9.00 pm on Friday nights,

the arrivals of customers are Poisson distributed with an average arrival rate of 3 per

minute.

a) What is the probability that at least 2 minutes will elapse between arrivals?

b) What is the expected amount of time between arrivals? Its standard deviation?

10. (a) “If you know that the probability that a normal variable exceeds a certain number

Q, is 0.10, you can be sure that this variable is less than –Q is also 0.10.”Do you

agree? Why or why not?

(b) It was reported that the average annual amount American households spend for

daily transportation is $6312. Assume that the amount spent is normally

distributed.

i). Suppose you learn that 5% of American households spend less than $1000 for daily transportation. What is the standard deviation of the amount spent? Using this fact answer:

ii) What is the probability that a household spends between $4000 and $8000?

iii) What is the range of spending for the 3% of households with the highest daily transportation cost?

i have tried to attempt these questions and have answers for some of them, but i am not sure if i am correct. please help me!

thank you so much in advance