Kay listens to either classical or country music every day while she works. If she listens to classical music one day, there is a 57% chance that she will listen to country music the next day. If she listens to country music, there is a 75% that she will listen to classical music the next day.

. All of the same information about Kay's listening habits remain true. However, suppose you know the additional fact that on a particular Monday the probability that she is listening to classical music is 0.2. (e) Based on your additional knowledge that there is a 0.2 probability that she is listening to classical music on Monday, what is the probability she will be listening to country music on Wednesday? (f) Based on your additional knowledge that there is a 0.2 probability that she is listening to classical music on Monday, what is the probability that she will be listening to classical music on Thursday?

The optimal scheduling of preventative maintenance tests of some (but not all) of n independently operating components was developed. The time (in hours) between failures of a component was approximated by an exponentially distributed random variable with mean 1300 hours. [Round to 4 decimal places where necessary.]

1. Find the probability that the time between a component failures ranges is at least 1600 hours.
2. Find the probability that the time between a component failures ranges between 1600 and 1900 hours.

3. Suppose a component is still working after 1600 hours, find the conditional probability that it will fail before 1900 hours.

4. If 9 components are tested, find the probability that at least 2 of them failed between 1600 and 1900 hours

5. Suppose 9 components are tested. What is the probability that 2 of them failed between 1600 and 1900 hours?

A small town has 7000 adult males and 5000 adult females. A sociologist conducted a survey and found that 60% of the males and 50% of the females drink heavily. An adult is selected at random from the town. (Enter your probabilities as fractions.)

(a) What is the probability the person is a male?


(b) What is the probability the person drinks heavily?


(c) What is the probability the person is a male or drinks heavily?


(d) What is the probability the person is a male, if it is known that the person drinks heavily?

Two balls are drawn from a bag containing 4 white balls and 3 red balls. If the first ball is replaced before the second is drawn, what is the probability that the following will occur? (Enter your probabilities as fractions.)

(a) both balls are red


(b) both balls are white


(c) the first ball is red and the second is white


(d) one of the balls is black

Suppose a binary message is transmitted through a noisy channel. The transmitted signal S has uniform probability to be either 1 or −1, the noise N follows normal distribution N(0,4) and the received signal is R=S+N . Assume the receiver conclude the signal to be 1 when R>=0 and -1 when R<0 .

1. What is error probability when one signal is transmitted?

2. What is error probability when one signal is transmitted if we triple the amplitude of the transmitted signal? It means S=3 or -3 with equal probability.

3. What is the error probability if we send the same signal three times (with amplitude 1), and take majority for conlusion? For example, if three received signal was concluded 1, −1, 1 by receiver, we determine the transmitted signal to be 1.

This is a very confusing question please show work!

Do the following using R. You must also turn in a copy of your R code.

(10) What is the probability a beta (1, 8) random variable is less than 0.13?

(11) What is the probability a beta (3, 9) random variable is greater than .4?

(12) What is the probability a beta (18,4.4) random variable is between 0.6 and 0.7?

(13) At what value of x is the probability that a beta (4, 7) random varable is less than x equal to .71? That is, for what x is P r(beta(4, 7) random variable < x) = .71?

(14) At what value of x is the probability that a beta (12.2, 25.7) random variable is less than x equal to .2? That is, for what x is P r(beta(12.2, 25.7) random variable < x) = .2?

QUESTION 16

A company that produces Headphones has two different plant locations, one located in North Carolina and one in Montana. In North Carolina there are 80 employees and in Montana there are 55 employees. The company wants to test their newest headphones and has decided to give away 30 pairs to a randomly selected group of employees. Compute the following probabilities.

What is the probability that half the headphones go to employees at the Montana plant?

QUESTION 17

What is the probability that at least 10 employees at the Montana plant receive headphones?

QUESTION 18

What is the probability that 15 or fewer employees at the North Carolina plant receive headphones?

QUESTION 19

What is the probability that fewer than 19 employees at the North Carolina plant receive headphones?

QUESTION 20

What is the probability that more than 15 employees at the Montana plant receive headphones?

Provide an example of a probability distribution of discrete random variable, Y, that takes any 4 different integer values between 1 and 20 inclusive; and present the values of Y and their corresponding (non-zero) probabilities in a probability distribution table.

Calculate: a) E(Y)

b) E(Y2 ) and

c) var(Y).

d) Give examples of values of ? and ? , both non-zero, for a binomial random variable X. Use either the binomial probability formula or the binomial probability cumulative distribution tables provided in class calculate:

a) ?(? = ?0) where ?0 is an integer of your own choice satisfying 0 < ?0 < ?. b) ?(? > ?0)

e) Suggest any value, ?0, of the standard normal probability distribution (correct to two decimal places), satisfying 1.10 < ?0 < 2.5 and then calculate:

a) P(Z> −?0) and b) P (Z< 0.8?0)

According to a study done by Nick Wilson of Otago University​ Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is

0.267. Suppose you sit on a bench in a mall and observe​ people's habits as they sneeze. Complete parts​ (a) through​ (c).

​(​a)

Using the binomial​ distribution, what is the probability that among 16 randomly observed​ individuals, exactly 6 do not cover their mouth when​ sneezing?

The probability is....________

​(Round to four decimal places as​ needed)

b) What is the probability that among 16 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

c) fewer than half of 16 individuals covering their mouth _____ be surprising because the probability of observing fewer than half covering their mouth when sneezing is
________, which ______ an unusual event

(round to four decimals!!!!)

.

A road averages 2,895 vehicles per day with a standard deviation of 615 vehicles per day. A traffic counter was used on this road on 34 days that were randomly selected.

a. What is the probability that the sample mean is less than 2,700 vehicles per​ day?

b. What is the probability that the sample mean is more than 2,900 vehicles per​ day?

c. What is the probability that the sample mean is between 2,800 and 3,000 vehicles per​ day?

d. Suppose the sample mean was 3,100 vehicles per day. Does this result support the stated population mean for this​ road?

The probability that the average vehicles per day is more than 3,100 is _____.  The result (does or does not)

support the findings because this probability is (less than or equal to; greater than) 0.05.

​(Type an integer or decimal rounded to four decimal places as​ needed.)