Math Answers

A sample of 60 Grade 9 students’ ages was obtained to estimate the mean age of all Grade 9 students. Sample mean of 15.3 years and the population standard deviation is 4. What is the point estimate of the population mean

Consider the sample 14, 19, 18, 20, 16, 9, 10, 6, and 8. Find the mean.

solve the cubic equation 2z³ -5z²+z-5=0

Show that (~𝒑∨𝒒)∧(𝒑∧~𝒒) is a contradiction

Convert (3–√,−1) into polar coordinates (r,θ) so that r≥0 and 0≤θ<2π

two good dice are rolled simultaneously. let a denote the event “ the sum shown is 8" and b the event “the two show the same number". find p(a), p(b), p(a ∩ b), and p(a ∪ b).

Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 19 of the 49 boxes on the shelf have the secret decoder ring. The other 30 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?

Question 1.13 [2, 2, 3]

Due to COVID-19 there was no time to have the swimming gala at your old primary school. The

principal knows that you are currently studying statistics and he wants you to help with this

probability problem. The principal tells you that out of the 8 swimmers, 3 are from grade 4, 2 are

from grade 5 and 3 are from grade 6. Since no Gala can be held the principal selects swimmers at

random to attend the EP school Gala, the first student selected at random will be representing the

schools fastest swimmer, while the second student selected will represent the school second fastest

swimmer.

Help the principal to answer the following questions:

a) What is the probability that the two fastest swimmers are from Grade 6?

b) What is the probability that fastest swimmer is from Grade 4 and the second fastest from

Grade 6?

c) Timothy is a student in grade 5, what is the probability that he will either come first or second?

Question 1.12 [2, 3]

Catherine has a Gmail account and categorises her emails according to work and non-work related

emails. The probability that an email is a work-related email is 65.32%. Suppose furthermore it is

given that the probability that a work-related email received is a spam email is 15.34% and that if it

is a non-work related email that it is spam is 5.6%.

Calculate the following probabilities

a) That an email received by Catherine is a spam email.

b) Given that the email is spam what is the probability that it is a non-work-related email.

Question 1.11[4]

There are two bags of chocolates. Bag one has 5 Barones and 2 KitKats and Bag 2 has 2 Barones

and the 7 KitKats. A chocolate is selected at random from Bag one and added to Bag two. A

chocolate is now drawn randomly from Bag two. Given that the chocolate selected is a KitKat what

is the probability that the original chocolate drawn from Bag one was a Barone? Show all working

out.