1. The number of hours that biology students study per week is normally distributed with a mean of 15 hours and a standard deviation of 5 hours.

a. Draw an approximate picture of the distribution of weekly hours studied for biology students.

b. If a student is chosen at random, what is the probability that the student studies less than 11 hours per week? Include a picture that graphically shows the portion of students that study less than 11 hours per week.

c. If a student is chosen at random, what is the probability that the student studies more than 20 hours per week? Include a picture that graphically shows the portion of students that study more than 20 hours per week.

d. What is the proportion of students that study between 8 and 20 hours per week? Include a picture that graphically shows this.

After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only two women among the last 22 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women. Help her address the charge of gender discrimination by finding the probability of getting two or fewer women when 22 people are hired, assuming that there is no discrimination based on gender. (Report answer accurate to 8 decimal places). P(at most two) = .00021 Incorrect Because this is a serious claim, we will use a stricter cutoff value for unusual events. We will use 0.5% as the cutoff value (1 in 200 chance of happening by chance). With this in mind, does the resulting probability really support such a charge?

A review of an airline operations revealed tat, historically, the airline had an average of 6.42 mishandled bags per 1.000 passengers. A mishandled bag is luggage that was not sent the passengers plane. It was either lost or arrived late.

a)What ise the chance that for the next 2.000 passengers,the airline will have more than 11 mishandled bags is?

b)After a consulting company evaluated the airlines operations, the airline overhauled its bag- monitoring compute system. As a result the number of mishandled bags or 1000 passengers decreased 30% . Given that new compute system, what is probability that for the next 2.000 passengers, the airline will have fever than 10 mishandled bags?

c)Given the new computer system, the probability that for the nex 3,000 passengers, the airline will have fewer 10 mishandled bags is?

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 30 weeks. Assume that the length of unemployment is normally distributed with population mean of 30 weeks and the population standard deviation of 6 weeks. Suppose you would like to select a random sample of 8 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the probability that one randomly selected individual found a job more than 28 weeks?
4. For 8 unemployed individuals, find the probability that the average time that they found the next job is more than 28 weeks.
5. For part d), is the assumption of normal necessary?

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 28 weeks. Assume that the length of unemployment is normally distributed with population mean of 28 weeks and the population standard deviation of 9 weeks. Suppose you would like to select a random sample of 35 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places.

What is the distribution of X? X ~ N

What is the distribution of ¯x? ¯x ~ N

What is the probability that one randomly selected individual found a job more than 30 weeks?

For 35 unemployed individuals, find the probability that the average time that they found the next job is more than 30 weeks.

For part d), is the assumption of normal necessary? yes or no

    In a certain hospital ER the average amount of patients that enter in a 15 minute interval is 3.6. If each 15 minute interval is independent of one another, and the amount of patients that show up in one 15 minute interval does not influence or change the number of patients that show up in any other 15 minute interval. Arrivals occur smoothly throughout each 15 minute interval. Answer the following questions:

A.            What is the probability that at most 2 patients will show up in a 15 minute interval?    

B.            What would be your new mean, if we were to use this information to figure out probabilities during a 5 minute interval?

C.            Using the new mean in part B, what is the probability that more than 1 patient will show up in a 5 minute interval?

Show your calculations in detail please..

1. Suppose that a researcher is conducting a study on fast food habits and assumes that 55% of adults prefer hamburger to pizza. He randomly selects 10 adults and ask whether they prefer hamburger to pizza or not. Based on this information, answer the following questions.

a) (20 pts) Define the random variable (in words) and check whether it is a binomial random variable or not and write your conclusion. Explain your answer.

b) (10 pts) What is the probability that at least 8 adults prefer hamburger?

c) (10 pts) What is the probability that as most 3 adults prefer hamburger?

d) (15 pts) What is the expected number of people who prefer hamburger.

e) (15 pts) Calculate the standard deviation of this random variable and interpret it.

The number of earthquakes that occur per week in California follows a Poisson distribution with a
mean of 1.5.
(a) What is the probability that an earthquake occurs within the first week? Show by hand and
provide the appropriate R code.
(b) What is the expected amount of time until an earthquake occurs?
(c) What is the standard deviation of the amount of time until two earthquakes occur?
(d) What is the probability that it takes more than a month to observe 4 earthquakes? Show by hand
(you may simply leave it as an integral) and provide the appropriate R code.
(e) What is the median amount of time it takes for 5 earthquakes to occur? Show by hand (you may
simply leave it as an integral, but be sure to explain how to find the median) and provide the
appropriate R code.

Let us suppose that some article investigated the probability of corrosion of steel reinforcement in concrete structures. It is estimated that the probability of corrosion is 0.19 under specific values of half-cell potential and concrete resistivity. The risk of corrosion in five independent grids of a building with these values of half-cell potential and concrete resistivity. Let the random variable X denote number of grids with corrosion in this building. Determine the cumulative distribution function for the random variable X.

Round your answers to five decimal places (e.g. 98.76543).

f(x)=           with x < 0

f(x)=             with 0 <= x < 1

f(x)=             with 1 <= x < 2

f(x)=             with 2 <= x < 3

f(x)=             with 3 <= x < 4

f(x)=             with 4 <= x < 5

f(x)=             with 5 <= x

A survey asked parents of children aged ten and under how many birthday parties they attended last year. Let X represent the number of birthday parties. The probability distribution is given below. Find the mean and the standard deviation of the probability distribution using Excel. Round the mean and standard deviation to three decimal places.

x P(x) 1 0.0303 2 0.0639 3 0.0197 4 0.003 5 0.0164 6 0.0454 7 0.0981 8 0.0648 9 0.0657 10 0.0124 11 0.0118 12 0.0539 13 0.0497 14 0.0648 15 0.0373 16 0.0475 17 0.0224 18 0.0191 19 0.0088 20 0.0406 21 0.0445 22 0.1202 23 0.0597