It is known that a certain basketball player will successfully make a free throw 87.4% of the time. Suppose that the basketball player attempts to make 14 free throws. What is the probability that the basketball player will make at least 11 free throws?

Let XX be the random variable which denotes the number of free throws that are made by the basketball player. Find the expected value and standard deviation of the random variable.

  E(X)=
   σ=

Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you replace the card, and draw another card. You repeat this process until you have drawn 16 cards in all. What is the probability of drawing at least 7 spades?

For the experiment above, let XX denote the number of spades that are drawn. For this random variable, find its expected value and standard deviation.

E(X)=
   σ=

1.       The government of Philippines is proposing a new program to encourage banana farmers to reduce their use of chemicals. Let us assume the present cost of the program as 1,000,000 pesos per participant. The benefits of the program are the reduction in environmental cost estimated at a present value of 4, 000, 000 pesos per participant.

However, the number of farmers that will participate in the program is not known with certainty, and the success of the program in reducing environmental cost is also uncertain.

The following table provides 5 scenarios of a number of participants and the probability of achieving the benefits from reducing environmental cost.

a)      Use the scenario approach of sensitivity analysis to estimate the NPV

b)      Under which scenarios will the project be feasible?

c)      What advice will you give to the government of Philippines on the feasibility of the project?

In the 1992 presidential election, Alaska's 40 election districts averaged 1845 votes per district for President Clinton. The standard deviation was 562. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places.

a. What is the distribution of X? X ~ N(,)

b. Is 1845 a population mean or a sample mean? Select an answer Population Mean Sample Mean

c. Find the probability that a randomly selected district had fewer than 1894 votes for President Clinton.

d. Find the probability that a randomly selected district had between 1872 and 2162 votes for President Clinton.

e. Find the first quartile for votes for President Clinton. Round your answer to the nearest whole number.

In the 1992 presidential election, Alaska's 40 election districts averaged 1982 votes per district for President Clinton. The standard deviation was 578. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places.

a. What is the distribution of X? X ~ N(,)

b. Is 1982 a population mean or a sample mean? Select an answer Population Mean Sample Mean

c. Find the probability that a randomly selected district had fewer than 1978 votes for President Clinton.

d. Find the probability that a randomly selected district had between 2107 and 2224 votes for President Clinton.

e. Find the first quartile for votes for President Clinton. Round your answer to the nearest whole number.

n the 1992 presidential election, Alaska's 40 election districts averaged 2118 votes per district for President Clinton. The standard deviation was 578. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places.

a. What is the distribution of X? X ~ N(,)

b. Is 2118 a population mean or a sample mean? Select an answer Sample Mean Population Mean

c. Find the probability that a randomly selected district had fewer than 1960 votes for President Clinton.

d. Find the probability that a randomly selected district had between 2126 and 2364 votes for President Clinton.

e. Find the first quartile for votes for President Clinton. Round your answer to the nearest whole number.

14. (20 pts) This data shows the number of healthcare worker injuries in a hospital over the last 24 months.

The mean is 6.292.

(a) Using Goodness-of-fit test for Poisson, test if the data follows the Poisson distribution and determine λ.

(b) Using the mean computed from (a), Compute the probability that there will be more than 7 injuries next year.

(c) Using the mean computed from (a), compute the probability that there will be 5 or fewer injuries next year

Have you ever tried to get out of jury duty? About 25% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty.†

(a) If 11 people are called for jury duty, what is the probability that all 11 will be available to serve on the jury? (Round your answer to three decimal places.)


(b) If 11 people are called for jury duty, what is the probability that 5 or more will not be available to serve on the jury? (Round your answer to three decimal places.)


(c) Find the expected number of those available to serve on the jury. What is the standard deviation? (Round your answers to two decimal places.)

(d) How many people n must the jury commissioner contact to be 95.9% sure of finding at least 12 people who are available to serve? (Enter your answer as a whole number.)
people

The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts​ (a) through​ (d) below.

Click the icon to view the table.

a. Find the probability of getting exactly 6 girls in 8 births.

nothing

_____ ​(Type an integer or a decimal. Do not​ round.)

number of girls (x) P(x)

How many people do you expected to arrive during a 45min period?Suppose that trees are distributed in a forest according to a two-dimensional Poisson process with parameter λ, the expected number of trees per acree, equal to 80.

1. What is the probability that in a certain quarter-acre-plot, there will be at most 16 trees?
2. If the forest covers 85,000 acres, what is the expected number of trees in the forest?
3. Suppose you selected a point in the forest and construct a circle of radius 0.1 mile. Let X = the number of trees within that circular region. What is the pmf of X? (Hint: 1 sq. mile = 640 acres.)

1.)

Forty

individuals independently construct a

98

​%

confidence interval for the mean of a certain population. What is the expected number of individuals who will obtain confidence intervals that actually contain the mean of the​population

2.)Forty percent of the employees in a large corporation are registered in the​ corporation’s fitness program. If 3500 employees are selected at random from this​ corporation, what is the probability between 1410 and​ 1445, inclusive, will be registered in the fitness​ program? (Round to the nearest tenth of a​ percent.)

3.)

A

die

is to be tossed

291

times. Let X represent the number of times the

die

lands with

an odd number

showing. What is the

standard deviation

for​ X? (Round to the nearest​ hundredth.)