1. Jade is renovating his bathroom and as part of the renovations a plumber is required to install a new shower. The budget for this part of the renovations is $1000. An industry expert has told Jade that the probability that a randomly selected plumber in Auckland will be able to do the job for $1000 or less is 0.55, and that a list of plumbers located in Auckland is available from the Plumbers, Gasfitters and Drainlayers Board website. There are a very large number of plumbers in Auckland.

(a) Suppose that Jade randomly selects 10 plumbers from the list of Auckland plumbers. What is the probability that exactly 2 plumbers will be able to install the new shower for $1000 or less?Answer this question using the appropriate mathematical formula.

(b) What is the probability that Jade will have to call at least 4 plumbers to find one that can do the job for $1000 or less?
Answer this question using the appropriate mathematical formula.

(c) What is the expected number of calls that Jade will have to make to find a plumber who can do the job for $1000 or less? What is the variance of the number of calls?

(d) Of the plumbers that will install the shower for $1000 or less, the cost of the job (in dollars) has a uniform distribution on the interval (450,1000). What is the expected value and variance for the cost of installing the shower?

(e) Suppose that Jade wants to select a plumber close to where he lives. Within his suburb there are 10 plumbers available and of these, 6 would do the job for $1000 or less. What is the probability that Jade will have to call exactly 4 plumbers before finding one who will do the job for $1000 or less? (i.e. the 4th plumber called will do the job).

Which of the investments discussed has had the highest average return and risk premium? I Which of the investments discussed has had the highest standard deviation? I What is capital market efficiency? I What are the three forms of market efficiency?

You just purchased the lockbox below to store a spare set of keys for your house. It allows you to set a passcode using digits from 0 to 9:

How it works:

-Each digit is either ON or OFF, so pushing the same button twice removes it from the combination (as opposed to adding it a second time to the code). E.g. pressing 2, 7, 4 or pressing 2, 7, 3, 4, 3 would produce the same code: 274

-It is a mechanical lock box (not digital) so it does not recognize the order of the buttons pushed. E.g. pressing 4, 5, 8, 1 is the same as pressing 8, 1, 4, 5: both represent the same code (4581 = 8145)

-Pressing the CLEAR button clears the last code attempted (sets all digits to OFF)

a) Explain why the correct code cannot exceed 10 digits.

b) There is no manual that comes with the lockbox. Your friend thinks the code needs to be exactly 10-digits long. If this were true, explain why this would not be a good lock box.

c) What is the probability of randomly guessing the correct code on your first attempt? Explain how you arrived at your formula.

d) Another friend suggests using 9-digit codes over 2- or 3-digit codes as they are longer and better for security. Do you agree or disagree? Explain.

You just purchased the lockbox below to store a spare set of keys for your house. It allows you to set a passcode using digits from 0 to 9:

How it works:

-Each digit is either ON or OFF, so pushing the same button twice removes it from the combination (as opposed to adding it a second time to the code). E.g. pressing 2, 7, 4 or pressing 2, 7, 3, 4, 3 would produce the same code: 274

-It is a mechanical lock box (not digital) so it does not recognize the order of the buttons pushed. E.g. pressing 4, 5, 8, 1 is the same as pressing 8, 1, 4, 5: both represent the same code (4581 = 8145)

-Pressing the CLEAR button clears the last code attempted (sets all digits to OFF)

a) Explain why the correct code cannot exceed 10 digits.

b) There is no manual that comes with the lockbox. Your friend thinks the code needs to be exactly 10-digits long. If this were true, explain why this would not be a good lock box.

c) What is the probability of randomly guessing the correct code on your first attempt? Explain how you arrived at your formula.

d) Another friend suggests using 9-digit codes over 2- or 3-digit codes as they are longer and better for security. Do you agree or disagree? Explain.

Sunland Ltd. purchased a new machine on April 4, 2014, at a cost of $187,360. The company estimated that the machine would have a residual value of $16,000. The machine is expected to be used for 10,200 working hours during its four-year life. Actual machine usage was 1,400 hours in 2014; 2,000 hours in 2015; 2,400 hours in 2016; 2,300 hours in 2017; and 2,100 hours in 2018. Sunland has a December 31 year end.

Calculate depreciation for the machine under each of the following methods: (Round expense per unit to 2 decimal places, e.g. 2.75 and final answers to 0 decimal places, e.g. 5,275.)

(1) Straight-line for 2014 through to 2018.

(2) Diminishing-balance using double the straight-line rate for 2014 through to 2018.

(3) Units-of-production for 2014 through to 2018.

Which method results in the highest depreciation expense over the life of the asset? Highest net income? Highest cash flow?

select a method that results in the highest depreciation expense over the life of the asset

Straight-line method or Diminishing-balance methods or Units-of-production method or All three methods are the same or No Impact   

Which method results in the highest net income?

select a method that results in the highest net income   

Straight-line method or Diminishing-balance methods or Units-of-production method or All three methods are the same or No Impact

Which method results in the highest cash flow?

select a method that results in the highest cash flow                                                                     

Straight-line method or Diminishing-balance methods or Units-of-production method or All three methods are the same or No Impact

STAT_14_1

In the pitcher are balls of different colors.
The probability of accidentally taking a red-ball out of the pitcher is p: (0<p<1).

A. Remove from the pitcher, incidentally and with the possibility of return, six balls.
The probability that exactly one red ball came out is four times greater than the probability that no red balls came out at all.

1. Find the p value.
2. What is the probability that only the first, third, and fifth balls will be red?

B. Now they decided to take balls out of the pitcher, accidentally and with the possibility of return, until the first red ball came out

1. What is the probability of getting exactly five balls out of the pitcher?
2. What is the expectation of the number of non-red balls coming out of the pitcher?

C. Yoav decided to take balls out of the jug, accidentally and with the option of returning, until he removed 4 red balls (not necessarily in succession).
What is the probability that he will get exactly 9 balls?

Q-1)1 to 5 in bag A; 1 to 11 in bag B there are numbered cards. A random from the randomly selected bag card is selected. Since there is an odd number on the selected card, A
What is the probability of being chosen from the bag? Note: Make a tree diagram and
express your results with Bayes Theorem and
Confirm.

Q-2)ABCD is a rectangle whose long edge is twice the short edge. Long midpoint X of edge AB; The midpoint of the short edge AD is Y. This choice with the XAY triangle. A randomly selected point in a rectangle Find the probability of being selected in the XAY triangle.

Q-3)Ali and Ahmet are playing matches. Ali’s probability of winning the match
3 times the probability of winning. Ali and Ahmet’s chances of winning
Find and using the Binomial distribution:
a) In the event of 3 matches, the probability of Ali winning twice
You calculate.?
b) At least 1 win of Ali in case of 3 matches
Calculate the probability.?

Thanks

STAT 14_1:

In the jug there are balls of different colors.
The probability of accidentally taking out a red-ball from the jug is P
When (0<P<1)

a. Remove from the jug, incidentally and with return, six balls.
The probability that exactly one ball came out red is four times greater than the probability that no red balls came out.
i. Find the p.
ii. What is the probability that only the first, third, and fifth balls will be red?

b. Now they decided to take balls out of the jug, incidentally and with return, until the first red ball came out.
i. What is the probability of getting exactly five balls out of the jug?
ii. What does the number of non-red balls expect from the jug?

c. Yoav decided to take balls out of the pitcher, incidentally and with return, until he removed 4 red balls (not necessarily in succession)
What is the probability that he will get exactly 9 balls?

The epidemiology lab at the UVA Hospital is trying to estimate how COVID-19 is affecting African American communities living near the Hospital. They know that the infection rates of African Americans in the Baltimore area have been high, at 12% since March 2020. A small team of courageous researchers samples 12 people on the street in several areas near the Hospital – to ensure that they don’t know each other.

a. Please write out the values of the random variable X (the number of people who could be infected in the sample) and its probability distribution. Also draw a histogram of this probability distribution. Then, compute the mean using both the definitional formula and the special formula for this probability distribution.

b. What is the standard deviation of this sample? Compute this standard deviation using both the definitional formula and the special formula for this probability distribution.

c. What is the probability that exactly one-third of this sample is infected with COVID-19?

d. What is the probability that less than 3 students in this sample are infected with the virus?

e. If a much larger group of 110

A) A missile launched from a submarine hits a target with a probability of 0.5. If hits from three missiles are required to destroy the target,  What is the probability that 5 missiles will be launched before the target is destroyed?  What is the expected number of missiles launched before the target is destroyed?

B) The time in days between consecutive breakdowns of a machine is exponentially distributed with a mean of 5 days. What is the probability that exactly two repairs are needed during a given week? 2

C) You arrive at a bus stop at 10:00 am, knowing that the bus will arrive at some time uniformly distributed between 10:00 and 10:30 am. What is the probability that you will have to wait longer than 5 minutes for the bus to arrive?

D) The time taken to complete an exam follows a normal probability distribution with a mean of 60 minutes and standard deviation of 10 minutes. What is the probability that a randomly chosen student will complete the exam in 50 minutes or longer?

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