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Use taylors formula to find quadratic and cubic approximations of f(x, y) =exsin y at origin. Estimate the error of the approximations if modx less than equal to 0.1 and mod y less than equal to 0.1
1.A tea company appoints four salesman A.B.C.D and observes their sales in three seasons Summer, Winter and Monsoon. The figures(in lakhs) are given in the following table:
Seasons. A B C D
Summer. 45. 40. 38. 37
Winter. 43. 41. 45. 38
Monsoon. 39. 39. 41. 41
Carry out an analysis of variance.
A researcher claims that 20 year old women on a special diet will have an average weight of 110 pounds. A sample of 15 women has an average weight of 112.5 pounds and a standard deviation of 5 pounds. A α = .01, can the claim be rejected?
Suppose that the thickness of a part used in a semiconductor is its critical dimension and that measurements of the thickness of a random sample of 18 such parts have the variance S2 = 0.68, where the measurements are in thousandths of an inch. The process is considered to be under control if the variation of the thickness is given by a variance not greater than 0.36. Assuming that the measurements constitute a random sample from a normal population, test the claim at the α =0.05 significance level.
With individual lines at its various windows, a post office founds that the standard deviation for normally distributed waiting times for customers on Friday afternoon is 7.2 minutes. The post office experiments with a single main waiting line and founds that for a random sample of 25 customers, the waiting times for customers have a standard deviation of 3.5 minutes. With a significance level of 5%, test the claim that a single line causes lower variation among waiting times (shorter waiting times) for customers.
A pet store keeps track of the purchases of customers over a fours hour period. The store manager classifies purchases as containing a dog product, a cat product, a fish product, or product for a different kind of pet. He found!
83 purchased a dog product
101 purchased a cat product
22 purchased a fish product
31 purchased a dog and a cat product
8 purchased a dog and a fish product
10 purchased a cat and a fish product
6 purchased a dog, a cat, and a fish product
34 purchased a product for a pet other than a dog, cat, or fish.
Draw a Venn diagram to find that:
(1) How many purchases were for a dog product only?
(ii) How many purchases were for a cat product only?
How many purchases were for a dog or a fish product?
(iv) How many purchases were there in total?
The heights of preschool children as reported by the Department of Statistics is approximately normally distributed about a mean of 39 inch and a standard deviation of 2 inch.
- What is the probability that the mean value is more than 40.0 inch?
- A random sample of size 25 is taken. What is the probability that the mean 𝑋̅ is more than 40.0 inch?
- Why is the answer for (b) is smaller than (a)?
- Within what limits does the middle 90% of the sampling distribution of sample means for samples of size 100 fall?
Determine how many bit strings of length 5 can be formed, where the first bit is 0 and three consecutive 0s are not allowed.
Based on a poll, among adults who regret getting tattoos, 17% say that they were too young when they got their tattoos. Assume that nine adults who regret getting tattoos are randomly selected, and find the indicated probability.
y=2x5+4x2) (x+5)
