Suppose that in an assortment of 30 calculators there are 5 with defective switches. Draw with and without replacement. (Enter the probabilities as fractions.)

(a) If one machine is selected at random, what is the probability it has a defective switch?

with replacement

without replacement

(b) If two machines are selected at random, what is the probability that both have defective switches?

with replacement

without replacement

(c) If three machines are selected at random, what is the probability that all three have defective switches?

with replacement

without replacement

Japanese automobiles comprise approximately 20% of all new car sales in the United States. Suppose a state licensing office received 100 requests for license plates for new cars during a given week.

      a) What is the probability that 25 or more of the license requests are for Japanese cars?

      b) What is the probability that no more than 10 of the requests are for Japanese cars?

      c) What is the probability that at least 10, but no more than 20, Japanese cars are represented within the group?

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 0.15. 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.

Explain in your own words the difference between a discrete random variable and continuous variable. Give a clear for example  for each that defines that distinct difference. 

What does it mean to have a success vs a failure? What the requirements for performing a binomial probability experiment? How do you find the mean and standard deviation of a binomial probability distribution? 

discussed probability, what does Do not give a formula - explain the formula itself and use an example to show this. 

Students interests. A student is chosen at random. Let A, B and C to be events that the student is an Accounting major, a Baseball player, or a Computer Science club member. The events are independent, and we are told that:

P(A)=P(B)=P(C)=0.17

a.Discuss if A and B are mutually exclusive events.

b.Find the probability that the student is not an Accounting major.

c.Find the probability that the student is a Baseball player or a Computer Science club member.

d.Find the probability that the student participates in at least one of these three programs.

At central hospital, there is a 27% chance that a patient will get an infection. We take a random sample of 25 patients. Find the following probabilities. (round all answers to 4 decimal places)

a. What is the probability that 3 or fewer of the patients will get an infection?

b. Find the probability that more than 10 of the patients will get an infection.

c. How likely is it that less than 6 would get an infection?

d. Compute the probability that at least 9 patients will get an infection.

A lap top computer manufacturer tests each device before leaving the factory. From history we know that the probability of failure is 0.9. If four laptops are randomly selected:

(1) what is the probability of fewer than 2 laptops fail the inspection?

a. 0.0037

b. 0.0058

c. 0.0074

d. 0.0024

(2) what is the probability that the third laptop which fails is the 4^th selected for inspection?

a. 0.2187

b. 0.7516

c. 0.3758

d. 0.4374

In the EAI sampling problem, the population mean is $51,600 and the population standard deviation is $5,000. When the sample size is n = 30, there is a 0.489 probability of obtaining a sample mean within +/- $600 of the population mean. Use z-table.

1. What is the probability that the sample mean is within $600 of the population mean if a sample of size 60 is used (to 4 decimals)?
   
   
2. What is the probability that the sample mean is within $600 of the population mean if a sample of size 120 is used (to 4 decimals)?

For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 3 systems detects theft with a probability of 0.84 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs, at least one of the 3 systems will detect it. What is the probability that when a theft occurs, at least one of the 3 systems will detect it? Your answer should be rounded to 5 decimal places.

In the EAI sampling problem, the population mean is 51,600 and the population standard deviation is 5,000. When the sample size is n=30, there is a 0.4176 probability of obtaining a sample mean within +/- 500 of the population mean.

1. What is the probability that the sample mean is within 500 of the population mean if a sample of size 60 is used (to 4 decimals)?

2. What is the probability that the sample mean is within 500 of the population mean if a sample of size 120 is used (to 4 decimals)?