1. A Private firm reports that 8% of the 2 million small businesses who apply for loan each year receive special interest rate (usually higher than market rate) because of high riskiness associated with small business. Consider a random sample of 25 small businesses who have recently applied for the loan

a. What is the probability that exactly 1 received a special interest?
b. What is the probability that at least 1 received a special interest rate?
c. What is the probability that at least 2 received a special interest rate?

2. The crop yield for a particular farm in a particular year is typically measured as the amount of the crop produced per acre. For example, cotton is measured in pounds per acre. It has been demonstrated that the normal distribution can be used to characterize crop yields over time. Historical data indicate that next summer's cotton yield for a particular Georgia farmer can be characterized by a normal distribution with mean 1,500 pounds per acre and standard deviation 250. The farm in question will be profitable if it produces at least 1,600 pounds per acre.
a. What is the probability that the farm will lose money next summer?
b. Assuming the same normal distribution is appropriate for describing cotton yield in each of the next two summers. Also assume that the two yields are statistically independent. What is the probability that the farm will lose money for two straight years?
c. What is the probability that the cotton yield falls within 2 standard deviations of 1,500 pounds per acre next summer?

Solution Summary

The solution provides step by step method for the calculation of binomial and normal probabilities. Formula for the calculation and Interpretations of the results are also included.

According to study done by Nick Wilson of Otago University, the probability a randomly selected individual will not cover his or her mouth when sneezing was 0.267. Suppose you sit on a mall bench and observe 200 people pass by as they sneeze.
1) Use the normal approximation to the binomial to find the probability of observing

Assume a binomial probability distribution has ยต=0.60 and n= 200
a. What is the mean and standard deviation?
b. Is this a situation in which binomialprobabilities can be approximated by the normal probability distribution? Explain
c. What is the probability of 100 to 110 successes?
d. What is the probability of 130 or

Question :
Assuming that X is a binomial random variable with n = 1000 and p = 0.50, find each of the following probabilities.
(a) P( X < 500 )
(b) P( 490 < X < 500 )
(c) P( X > 500 )
(d) P( X > 550 )

Determine if the normal approximation to the binomial distribution could be used for the following problems:
A.) A study found that 1% of Social Security recipients are too young to vote. 800 Social Security recipients are randomly selected.
B.) A study found that 30% of the people in a community use the library in one yea

A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute the probability of a value between 75.0 and 90.0. Compute the probability of a value 75.0 or less. Compute the probability of a value between 55.0 and 70.0.
In a binomial situation n = 4 and p = .25. Determine the probabilities of the following e

Population of consumers where 30% of them favored a new product and 70% of them disliked it. If 20 persons are sampled, what are the probabilities of finding: Binomial: 8 or fewer consumers who favor the product. Precisely 10 consumers who favor the product. Fewer than 6 consumers who favor the product. More than 7 consumers who

h-p is said to be the leading seller of pc's in the U.S WITH 27% share of the pc market. if a researcher selects 130 recent pc purchases, use the normal approximation to the binomial to find the probability that more than 39 bought a h-p computer

Please use words to describe the solution, not just symbols. (basically, explain what is going on in addition to an answer) Use a math symbol editor where appropriate.
Problem 1:
Write a program to compute binomialprobabilitiesand compare the results with the Poisson approximation for the following cases:
a) P(X = 2)

1. Infectious disease question:
Evaluate the probabilities of obtaining k neutrophils out of 5 cells for k=0,1,2,3,4,5 where the probability that any one cell is a neutrophil is 0.6. Find the expected number and standard deviation of neutrophils of the 5 cells.
2. Pulmonary disease question:
Compute the probability of obta

Please show all work and examples
1. Under certain conditions, it is possible that the sum of the probabilities of all the sample points in a sample space is less than one. ___ T/F
2. A compound event formed by use of the word and requires the use of the addition rule. ____ T/F
3. In any binomial probability