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?
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.