you will be assessed on the use of BINOM.DIST function, and creating formula to calculate the expected value of a binomial distribution. You will also be asked to interpret a probability value.

Multiple Choice Test

Chris is sitting a multiple choice test in statistics. The test consists of 9 items and each item has 5 options. After the test, Chris told you he didn’t study for the test at all and guessed all answers.

a)

If Chris guessed each and every item in the test, describe the probability distribution for the number of correct guesses. Present the probability distribution in the form of a table using 6 decimal points in your answers. (Use BINOM.DIST function to calculate the probabilities.)

In a recent poll, 38% of people said that chocolate was their favorite flavor of ice cream. Suppose that 20

     adults are randomly selected.                                                                                                                                             

1. Let X equal the number of people that answer chocolate is their favorite flavor of ice cream in the sample of 20. What is the probability distribution of X? (Be sure to list the specific distribution) (binomial, geometric, Poisson, exponential, uniform)   

2. How many adults would you expect to say that chocolate is their favorite ice cream flavor?               [2]

3. What is the standard deviation?                                                                                                                                 [2]

4. What is the probability that nine of these adults would say that chocolate is their favorite flavor?    [3]

5. What is the probability that at least 12 adults would say that chocolate is their favorite flavor?       [3]

a) Based on historical data, 9% of all logs arriving at a lumber mill are of suitable quality for use in timber frame construction. Also based on historical data, the average number of logs arriving at the mil per day is 33. Calculate, to the nearest %, the probability that 4 or more logs suitable for timber frame construction arrive at the mill on any given day. b) If 10 logs arriving at the mill are randomly selected, what is the probability, to the nearest %, that 4 or more of them will be suitable for timber frame construction? c) If a project requires 8 logs that are suitable for timber frame construction, what is the probability, to the nearest %, that enough of these logs arrive at the mill over the next 4 days?

Tom is making calls door to door in a neighborhood of 45 houses to give out gift cards for a new supermarket. He leaves a gift card only on those calls for which the door is answered. On any call the probability of the door being answered is 40%.

a) Find the probability that Tom gives away at most 2 gift cards in the first 5 calls.

b) Given that he has given away exactly 2 gift cards on his first 5 calls, find the probability that Tom will give away the 5th gift card on the 10th call.

c) Find the expected total number of cards given out when he is done.

A toll-free phone number is available from 9 a.m. to 9 p.m. to customers who want to register a complaint about a product purchased from your company. Past history indicates that, on average, 0.4 calls are received per hour.

(a) Decide what would be an appropriate distribution to describe the process [2] of people making complaints. Give a justification of your answer, in at most one sentence.

(b) Using the distribution in (a), find the following probabilities: (i) the probability that zero phone calls will be received; [4] (ii) the probability that one phone call will be received; [4] (iii) the probability that two or more phone calls will be received. [2]

Ch.3: Random Variable: nd Probability Distributions Class Exercise - A: The data from 200 endothermic reac ns involving sodium bicarbonate are summarized as follows: Final Temperature Conditions 266 K(48) 271 K(60) 274 K(92) Number of Reactions 48 60 92 Calculate the probability mass function of final temperature

Ch.3: Random Variable, and Probability Distributions Class Exercise - B:

Determine the cumulative distribution function for the random variable in Exercise A (In the previous slide)

Show the plot for this Cumulative Distribution Function.

please answer the questions A and B and please don't forget the chart in Exercise B

According to a report from a business intelligence​ company, smartphone owners are using an average of 23 apps per month. Assume that number of apps used per month by smartphone owners is normally distributed and that the standard deviation is 4. Complete parts​ (a) through​ (d) below.

A) If you select a random sample of 36 smartphone​ owners, what is the probability that the sample mean is between 22.5and 23.5?

B) If you select a random sample of 36 smartphone​ owners, what is the probability that the sample mean is between 22 and 23

C) If you select a random sample of 100 smartphone​ owners, what is the probability that the sample mean is between 22.5 and 23.5​?

2. Tom is making calls door to door in a neighborhood of 45 houses to give out gift cards for a new

supermarket. He leaves a gift card only on those calls for which the door is answered. On any call the probability of the door being answered is 40%.

1. a) Find the probability that Tom gives away at most 2 gift cards in the first 5 calls.

2. b) Given that he has given away exactly 2 gift cards on his first 5 calls, find the probability that Tom

   will give away the 5th gift card on the 10th call.

3. c) Find the expected total number of cards given out when he is done.

1. If the number of arrivals at a cell phone kiosk has a rate of 0.80 customers per hour.

to. What is the probability that less than 2 clients arrive in the next half hour? (10 points)

b. What is the probability that in the next three hours between 2 and 4 clients will arrive inclusive? (10 points)

c. Last customer arrived at 2:00 pm, what is the probability that the next customer takes more than 60 minutes to arrive? (10 points)

d. What is the average time between arrivals in minutes? (5 points)

and. What is the medina of the time between arrivals? (5 points)

F. What is the 80% percentile? (5 points)

In 2018-2019 season, Adam had a free throw success percentage of 64.2%. Assume that free throw shots are independent and that he had 8 free throws in a game.

Let X= number of free throws made in the next game.

-X has a binomial distribution, state the value of n and p.

-Find the binomial properties. Create a probability distribution table for X and show this probability distribution below.

(Write the following in terms of x in part A and in part B determine the probabability)

1. -Half are made

a. x=

b. Probabability=

2. Compute the mean and standard deviation for the probability distribution. Interpret the values that you calculate in the context of this problem.