Kola

If the mean is 100 and the standard deviation is 3%. What can the range of numbers around the mean be? Thanks

A class contains five muslim students and four christian students. One student is selected from the class at random; the student is asked to remain in class and a second student is selected. Find the probability of selecting:

a. Two muslim students

b. Two christian students.

c. Two students of the same religion.

d. Two students of different religion

An isoquant depicts the different combinations of inputs K and L that can be used to produce a specific level of output Q. One such isoquant for the output level Q = 2144 is:

16K^1/4 . L^3/4 = 2144

Use implicit differentiation to find the slope of the isoquant dK/dL which in economics is called the marginal rate of technical substitution (MRTS).

Consider a computer system with a job-arrival stream at an average of 2-per minute. Determine the probability that in any one-minute interval, there will be::

a. zero jobs

b. Exactly two jobs

c. At most 3 arrivals

d. What is the maximum jobs that should arrive one-minute with 90percent certainty??

a. How many different word can be formed with the letters of 'SKYSCRAPERS' if A and E are together

b. How many of the 'SKYSCRAPERS' word begin with 'K' and end with 'A'

The total scores in the examination into private schools are normally distributed with mean 300 and standard deviation 15.

Compute the probability that the score of a randomly selected student in the 2016 exam will be:

a. More than 330

b. Less than 235

c. At least 270 and at most 330

When f(x)= x^3+px^2+qx+r is divided by (x-1), (x+2) and (x-3) the remainders are -14, 16 and 36 respectively. Find the values of the constants p, q and r

A cricket team comprises of 11 players and other 3 players on the reserve bench.

1. How many ways can the coach select a team if the captain must be included and 2 other injured players must be excluded?

2. If the captain is to be excluded from the selection above and another of coach's favourite player must be in any team, how many ways can such 11 team be selected??

In how many ways can the word "HIPPOPOTAMUS" be arranged if

(1) "AMUS" are always together?

(2) it begins wit "H" and end with "S"

How many ways can the letters of the word "MOSHOESHOE" be arranged, if the letter "M" must always begin a word ??

Suppose there are two goods with prices P1 = 2, P2 = 5, the income is M = 40 and the utility function is U(X1, X2) = X1^(1/3).X2^(1/2). Find the optimum consumption plan

A manufacturer sends out 1000 lots, each consisting of 100 electric bulbs. If 5percent of the bulbs are normally defective, in how many of the lots should we expect

i). More than 90 good bulbs

ii) 98 or more good bulbs

The ratio of the interior angle to the exterior angle of a regular polygon is 5:2. Find the number of sides of the polygon.

Suppose a professor is carrying out a statistical research in New York and found out that the duration of marriages without the consent of parents have been found to be normally distributed with mean of 10 years and standard deviation of 3 years.

a. The probability is 0.80 that the mean of a random sample of 80 such marriages is between X₁ and X₂. Find X₁ and X₂ using symmetrical limits about the mean

Suppose a professor is carrying out a statistical research in New York and found out that the duration of marriages without the consent of parents have been found to be normally distributed with mean of 10 years and standard deviation of 3 years.

a. The probability is 0.80 that the mean of a random sample of 80 such marriages is between X₁ and X₂. Find X₁ and X₂ using symmetrical limits about the mean

Suppose a professor is carrying out a statistical research in New York and found out that the duration of marriages without the consent of parents have been found to be normally distributed with mean of 10 years and standard deviation of 3 years.

a. Find the probablity that a single marriage of this nature would last longer than 18 years.

b. What is the probability that the mean of a simple random sample of 50 such marriages would not last longer than 9 years?

c. The probability is 0.80 that the mean of a random sample of 80 such marriages is between X₁ and X₂. Find X₁ and X₂ using symmetrical limits about the mean

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A number is selected at random from each of the set {2, 3, 4} and {1, 3, 5}. Find the probability that the sum of the two numbers is greater than 3.

if f(x) = 2x - 1, g(x) = 3 - 2x and h(x) = 1/4(5-x)

a. Find a formula for k(x) where k(x) = f[g(x)]

b. Find a formula for h[k(x)]

Solve y(y+1) + 12/[y(y+1)] =8