Let X ~ Geom(p), let n be a non-negative integer, and let Y ~ Bin(n, p). Show that P(X = n) = (1/n)P(Y = 1).
What will be an ideal response?
(a) The proportion of strengths that are less than 65 is 0.10. Therefore 65 is the 10th percentile of strength. The z-score of the 10th percentile is approximately z= ?1.28. Let ?be the required standard deviation. The value of ? must be chosen so that the z-score for 65 is ?1.28. Therefore ?1.28 = (65 ? 75)/?. Solving for ? yields ?= 7.8125 N/
.
(b) Let ? be the required standard deviation. The value of ?must be chosen so that the 1st percentile of the distribution is 65. The z-score of the 1st percentile is approximately z= ?2.33. Therefore ?2.33 = (65?75)/?. Solving for ?yields ?= 4.292 N/
.
(c) Let ? be the required value of the mean. This value must be chosen so that the 1st percentile of the distribution is 65. The z-score of the 1st percentile is approximately z= ?2.33. Therefore ?2.33 = (65 ? ?)/5. Solving or ? yields ?= 76.65 N/
.
You might also like to view...
Concrete block have become very popular with landscaping masonry contractors and home owners for many uses.
Answer the following statement true (T) or false (F)
In the automotive service industry there is a shortage which type of employees?
A) Office Managers B) Technicians C) Owners D) Cashiers
On a typical in-line 6 cylinder, 4-stroke cycle diesel engine, when piston #5 is at TDC on it's compression stroke, which valves can be adjusted?
A. #5 B. #2 C. #4 D. #6
The National Research Council has concluded that CLA is the only fatty acid shown to inhibit carcinogenesis in animals
Indicate whether the statement is true or false