Math Answers

The packaging on an electric light bulb states that the average length of life of bulbs is 1000 hours. A consumer association thinks that this is an overestimate and tests a random sample of 64 bulbs, recording the life x

 hours, of each bulb. The results are summarised as follows:

∑x=63910.4,∑x2=63824061

Calculate an unbiased estimate for the standard deviation of the length of life of all light bulbs of this type.

4x-3y+z=-8

-2x+y-3z=-4

x-y+2z=3

Halwings Group Ltd, a company operating in Kenya has the following information as at 1st December 2020;

i. The company made a profit before tax of Ksh. 14,000,080 in the past 12 months of accounting

ii. The company made a net book loss of Ksh.1,100,050 in the year 2019

iii. The company engaged in consultancy services in the year 2020 where they were paid Ksh. 5,000,000

iv. The company supplied vaatable goods worth Ksh. 3,500,000 and Ksh. 9,000,000 in the years 2019 and 2020 respectively

From the information below concerning an employed Kenyan on a pension scheme, calculate the gross pay, chargeable pay, tax charged and PAYE for the individual (Clearly explain and show your workings)

Description AMOUNT

Basic Pay 163,562

ALLOWANCE

Housing Amount 139,675

Commuting Allowance 10,000

Gross Pay ???

TAX CALCULATIONS

Defined Contributions 200

Provident Fund 16,356.2

Taxable Pay ???

Tax Charged ???

Personal Relief 1,408

STATUTORIES

N.S.S.F 200

N.H.I.F 1,700

P.A.Y.E ???

. A rocket has a mass of 4.29*106 kg on earth. What is its mass in SI units? What is its weight in SI units? If the rocket is on the moon, where acceleration due to gravity is g = 1.61 m/s2 , determine its mass and its weight on the moon in SI units.

Ask about the lenght of 5 formed using the lettre ABCDEFG without repetitions. How many string begins with the letter F and end with the letter A

A sandwich shop serves 4 ounces of meat and 3 ounces of cheese on each sandwich. After making sandwiches for an hour, the shop owner has used 91 combined ounces of meat and cheese.

Suppose a statistician chose to test a hypothesis at ∝= 0.01. The critical value for a right-tailed test is +2.33. If the test value were 1.97, what would the decision be? What would happen if, after seeing the test value, she decided to choose ∝= 0.05? What would the decision be? Explain the contradiction if there is one.

Run these commands in R, then use your own words to describe what the resulting numbers represent. You can get some information about the functions by using the help commands in R (such as ?pbinom to get information about the pbinom() command in R):

a) pbinom(q=5, size=10, prob=1/6)

b)

n=10

p=.5

x=9

pbinom(x, n, p)

c) punif(5, min=1, max=10) - punif(4, min=1, max=10)

Vocabulary and R functions

We are now covering material that is not common knowledge, and it is now very important to include citations when you use an idea from another source (book, Internet, etc). Be sure to add a citation and reference entry for the definition questions below.

a) What is an exponential distribution (include an APA citation)? ___________________________

b) When would you use an exponential distribution? ________________________

c) What is a binomial distribution (include an APA citation)?_______________________

d) When would you use a binomial distribution? ___________________