Math Answers

From the past experience, a prof knows that the test score of a student taking his final xm is a random variable with mean 75 and variance 25.what os can be said about the probability that a student will score between 65 and 85.

You intercept the message "KVW?TA!KJB?FVR."(The blanks after? and R are part of the message,but the final is not.You know that a linear enciphering transformation is being used with a 30- letter alphabet, in which A-Z have numerical equivalents 0-25, blank=26, ?=27, !=28, .=29.You further know that the first six letters of the plain text are "C.I.A". Find the deciphering matrix A inverse and the full plain text message.

A sample random sample of size 4 is drown with replacement from a population with s.d. 6 what is the S. E of the sample mean?

You are the Manager of a new computer manufacturing company, Fongkomputer. Tests have shown that the mean life time of your computers is normally distributed, and on average your computers last for only 9 months, with a standard deviation of 3 months. The managing director wants the chance of computer being returned within its guarantee period to be 10%. Suggest a guarantee period that will achieve this objective. Round your solution to the nearest month

Find two numbers whose sum is 24 such that the sum of the square of one plus six times the other is a minimum.

A small jewelry box with square of base is to have a volume of 125 cu.cm. Find its dimensions to require the least amount of material.

Using thye following information: H_0:=375; H_a: 375; n=100; x = 390; ²=4,900 and a =0.05. is the z-test statistic value equal to 2.14?

About how many % of scored distribution is between z=0 and z=1?

Find P(-1.2 <2<-0.2)

a) A three digit number is to be formed using the digits 1, 2, 3, 4, 5, 6 and no repetition is

allowed.

i) How many numbers can be formed if the leading digit is 4?

ii) How many numbers can be formed if the number is more than 250?

iii) How many odd numbers can be formed between 200 and 400?

(8 marks)

b) Consider a bookshelf contains 28 books in different genre. 14 books are in education, 9

books in business and 5 books in motivation. A student would like to take 15 books. Find the number of ways if:

I) there is no restriction

ii) the choice must consist of 8 books in education, 5 books in business and 2 books in

motivation genre.

iii) The choice must consist of at least 9 books in education and exactly 5 books in

motivation genre.

(7 marks)