A binomial experiment is a series of n successive Bernoulli trials (a repetition of a success/failure experiment n times). The discrete probability distribution of the number of successes in these trials is known as a binomial distribution. The simplest form, when only one trial is performed, is a Bernoulli distribution. The formula for calculating the probability of k successes in n trials is , where the binomial coefficient is the number of ways k things can be chosen from a set of n items. An example of a binomial distribution is when flipping a coin 10 times and counting heads, the distribution is and . The mean of a binomial distribution (μx) equals np, and the variance () equals .
in the problem below find a 95% prediction interval for Y when X1=75 and X2=70 assuming that Ei's are normally distributed with mean zero ad variance sigma squared.
a study was made of the relationship among skein strength (Y, in lb) of #225 cotton yarn, mean fiber length (X1 in 0.01 inch) and fiber tesile strength (X2 in 1000 psi). Twenty combinations of X1 and X2 values were used and Y observed at each of these combinations. The observations yield the following results: look at the picture
Two separate samples receive different treatments. After treatment, the first sample has n = 9 with SS = 462, and the second has n = 7 with SS = 420.
a. Compute the pooled variance for the two samples.
b. Calculate the estimated standard error for the sample mean difference.
c. If the sample mean difference is 10 points, is this enough to reject the null hypothesis using a two-tailed test with ? = .05?•
a researcher selects a sample of n = 25 college students. Each student is given a ginkgo biloba supplement daily for six weeks and then all the participents are given a standardized memory test. For the population, scores on the test are normallt distributed with Î¼ = 70 and Ï� = 15. The sample of 25 students had a mean score of M = 75. Are the data sufficient to claim that the herb has a significant effect on memory? Use a two-tailed test with Î± = 0.05.•
Minimize: In a cattle ranch, Two types of food, brand A and brand B are going to be mixed. Each serving is required to have 60 % protein and 30 % fat. The problem is that How much of each type should be used to minimize the cost?
Suppose that brand A contains 15% protein and 10% fat with a cost of $8 per pound and brand B has 20 % protein and 5% fat, and costs $5 per pound.
- Formulate a linear programming model for this problem. (Type on an excel spreadsheet )
- Solve this problem graphically. ( Excel)
- Use excel solver to find the optimum solutions. ( on a separate spreadsheet)
Join Chegg Study
Guided textbook solutions created by Chegg experts
Learn from step-by-step solutions for 2,500+ textbooks in Math, Science, Engineering, Business and more
24/7 Study Help
Answers in a pinch from experts and subject enthusiasts all semester long