A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the table.

What is the probability of between 1 and 3 (inclusive) complaints received per week?

Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

3. A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the table.

What is the mean of complaints received per week?

Please round your answer to the nearest hundredth.

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

4. Let X be a discrete random variable. If Pr(X<9) = 3/8, and Pr(X<=9) = 7/16, then what is Pr(X=9)?

Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).

How to do this program in C ?

You have a sock drawer.  You have an infinite supply of red, green, yellow, orange, and blue socks.
1) Choose how many socks of each color you will put into the drawer.  0 is an ok number, but it would be nonsense to allow the user to put a negative number of socks into the drawer, so if the user tries to do that, print an error message and quit the program.

2) Ask the user to specify two colors of socks typing the first letters of the two colors in response to a prompt.  Sample dialog:

What two colors of socks are you interested in:YO
It is an error to specify the same color twice.  
Your response of YO would mean that you are interested in yellow and orange socks.
RR would be an improper response and should recieve an error message.

3) Pretend that the user shuts their eyes, reaches into the drawer, and retrieves one sock.  Calculate the probability that the sock is one of the two specified colors.

If c1 and c2 are the specified colors, and nk is the number of socks of color k,
then the required probability would be

(n1 + n2) / (n1 + n2 + n3 + n4 + n5)

For instance, suppose there are 5 red socks, 4 green socks, 3 yellow socks, 2 ornage socks and 1 blue sock. If the user specified red and yellow (RY)
the probability would be (5 + 3) / (5 + 4 + 3 + 2 + 1)

Use ints to hold the number of socks of each color, but calculate the
probabilities as doubles.

Suppose two people (let’s call them Julio and Karina) agree to meet for lunch at a certain restaurant, each person’s arrival time, in minutes after noon, follows a normal distribution with mean 30 and standard deviation 10. Assume that they arrive independently of each other and that they agree to wait for 15 minutes. If each person agrees to wait exactly fifteen minutes for the other before giving up and leaving.

h) Report the probability distribution of the difference (not absolute difference) in the arrival times of Julio and Karina. [Hint: You might let Tj represent Julio’s arrival time and Tk represent Karina’s arrival time, both in minutes after noon. Use what you know about normal distributions to specify the probability distribution of the difference D = Tj – Tk.]

i) Use appropriate normal probability calculations to determine the probability that the two people successfully meet. Also report the values of the appropriate z-scores. [Hint: First express the probability that they successfully meet in terms of the random variable D.]

j) Now let m represent the number of minutes that both people agree to wait, where m can be any real number. Determine the value of m so the probability of meeting is .9

k) Now suppose that Julio and Karina can only afford to wait for 15 minutes, but they want to have at least a 90% chance of successfully meeting. Continue to assume that their arrival times follow independent normal distributions with mean 30 and the same SD as each other. Determine how small that SD needs to be in order to meet their criteria. (As always, show your work.)

Problem 3-15 (Algorithmic) Telephone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. (a) Find the probability of receiving 6 calls in a 5-minute interval. If required, round your answer to four decimal places. f(6) = (b) Find the probability of receiving 8 calls in 15 minutes. If required, round your answer to four decimal places. f(8) = (c) Suppose that no calls are currently on hold. If the agent takes 4 minutes to complete processing the current call, how many callers do you expect to be waiting by that time? If required, round your answer to one decimal place. Number of callers = What is the probability that no one will be waiting? If required, round your answer to four decimal places. The probability none will be waiting after 4 minutes is . (d) If no calls are currently being processed, what is the probability that the agent can take 2 minutes for personal time without being interrupted? If required, round your answer to four decimal places. The probability of no interruptions in 2 minutes is .

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day. The numbers in the Table below represent the number of groups of dolphins that took part in an activity at certain times of days. In Excel

1. Calculate the probability (in reduced fraction form) that a dolphin group is involved with travel.
2. Calculate the probability (in reduced fraction form) that a dolphin group is around in the morning.
3. Calculate the probability (in reduced fraction form) that a dolphin group is involved with travel, given that it is morning.
4. Calculate the probability (in reduced fraction form) that a dolphin group is around in the morning, given that it is socializing.
5. Calculate the probability (in reduced fraction form) that a dolphin group is around in the afternoon, given that it is feeding.
6. Calculate the probability (in reduced fraction form) that a dolphin group is either around in the evening or is feeding.

An insurance company issues 1600 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 5. Assume the numbers of claims filed by distinct policyholders are independent of one another. Find the approximate probability that the number of total claims during a one-year period is between 7928 and 8197.

Show (prove, demonstrate, whatever) that the number of ways to obtain r "successes" (1's) in a series of n binary outcomes is equal to the combination nCr. For example, the number of ways to obtain 2 successes (1's) in a sequence of 3 binary digits is 3; or in a sequence of 4 bits is 6. This came up in our derivation of the binomial probability distribution; it is also covered in chapter 5.

Seventy percent of all vehicles examined at a certain emissions inspection station pass the
inspection. Suppose a random sample of 12 cars is selected. Assuming that successive vehicles
pass or fail independently of one another calculate each of the following.

a.)What is the expected number of vehicles to pass?

b.)What is the probability that the number of the 12 cars selected that pass is within one standard deviation of the expected value?