Assume the geometric distribution applies. Use the given probability of success p to find the indicated probability.

Find​P(5​) when p=0.60

​P(5​)=

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

2.

Given that x has a Poisson distribution with μ=5​, what is the probability that x=5​?

​P(5​)≈

3.

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.

Assume the probability that you will make a sale on any given telephone call is 0.23

Find the probability that you​ (a) make your first sale on the fifth​ call, (b) make your sale on the​ first, second, or third​ call, and​ (c) do not make a sale on the first three calls.

4.

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.

The mean number of births per minute in a country in a recent year was about

five. Find the probability that the number of births in any given minute is​ (a) exactly

six​, ​(b) at least six and​ (c) more than six.

Write a c++ program for the Sales Department to keep track of the monthly sales of its salespersons. The program shall perform the following tasks:

• Create a base class “Employees” with a protected variable “phone_no”
• Create a derived class “Sales” from the base class “Employees” with two public variables “emp_no” and “emp_name”
• Create a second level of derived class “Salesperson” from the derived class “Sales” with two public variables “location” and “monthly_sales”
• Create a function “employee_details” under the class “Salesperson” for obtaining the following information:
  • Employee number “emp_no”
  • Employee name “emp_name”
  • Employee phone number “phone_no”
  • Employee office location “location”
  • Monthly sales amount “monthly_sales”
• In the main() function, do the following:
  • Declare variables (int i, count, temp)
  • Create an object of Salesperson (ex. Salesperson man[50])
  • Prompt user to enter the number of salespersons
  • Create a for loop to loop through the number of salespersons to obtain the detailed info of the salesperson calling the “employee_details” function
  • Create a for loop to determine the salesperson with the highest sales
  • Print the results as below:
    • The highest monthly sales is : $100000
    • Congratulations!! Amy Ho! You are the top salesperson this month.
  • Create a for loop to determine the salesperson with the lowest sales
  • Print the results as below:
    • The lowest monthly sales is : $95876
    • Ramp Up, Brady Anderson. Your sales is the lowest this month.

Sample output:

How many salespersons you want to enter? :2

Enter details of employee

--------------------------

Enter employee No. :10

Enter employee name:Amy Ho

Enter employee phone No. :3134735678

Enter employee office location :Detroit

Enter monthly sales amount : $100000

Enter details of employee

--------------------------

Enter employee No. :20

Enter employee name:Brady Anderson

Enter employee phone No. :5156789876

Enter employee office location :Chicago

Enter monthly sales amount : $95876

The highest monthly sales is : $100000

Congratulations, Amy Ho! You are the top salesperson this month.

The lowest monthly sales is : $95876

Ramp Up, Brady Anderson. Your sales is the lowest this month.

Write a code in Python jupytoer note book:

Suppose approximately 75% of all marketing personnel are extroverts, whereas about 65% of all computer programmers are introverts. (For each answer, enter a number. Round your answers to three decimal places.)

(b)

In a group of 4 computer programmers, what is the probability that none are introverts?

What is the probability that 2 or more are introverts?
What is the probability that all are introverts?

United Airlines' flights from Boston to Seattle are on time 60% of the time. Suppose 10 flights are randomly selected, and the number on-time flights is recorded. Find the following probilities. (Round your answer to 4 decimal places.)


The probability that at least 3 flights are on time.

The probability that at most 4 flights are on time.

The probability that exactly 6 flights are on time.

Probability Mass Functions, Random Variables

Find a table of the Binomial random variable (include a picture of the table in your submission) and obtain the probability that in 20 independent trials, each of which has probability of success equal to 0.1, the number of successes is less than or equal to 3.

Repeat the problem using instead of a Binomial a Poisson with suitable parameter lambda.

Let X be the number of students who attend counseling at a certain time of day. Suppose that the probability mass function is as follows p (0) = .15, p (1) = .20, p (2) = .30, p (3) = .25, and p (4) = .10. Determine:

a) Is this a valid probability mass function? Why?

b) Obtain the cumulative probability function

c) What is the probability that at least two students come to counseling

d) What is the probability that, from one to three students, inclusive, they will come to counseling e) Obtain the average and standard deviation of the probability function. Interpret your results.