Search & Filtering
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 (~πβ¨π)β§(πβ§~π) is a contradiction
(6x+3y-5)dx+(2x+y)dy=0
Convert (3ββ,β1) into polar coordinates (r,ΞΈ) so that rβ₯0 and 0β€ΞΈ<2Ο
two good dice are rolled simultaneously. let a denote the event β the sum shown is 8" and b the event βthe two show the same number". find p(a), p(b), p(a β© b), and p(a βͺ b).
Two dice are thrown. Let A bet the event that the sum of the upper face numbers is odd, and B the event of at least one ace . Assuming a sample space of 36 points, list the sample points which belongs to the events A β© B , A βͺ B and A β© Ζ. Find the probabilities of these events, assuming equally likely events.
II. COMPUTATION SKILLS.
For item no. 29-32: Below is a sampling distribution of the sample means from the given problem. Check if the table is correct by listing all the possible samples and the corresponding mean.
Problem: A population consists of the five numbers 2,4,6 and 8. Consider samples of size 2 that can be
Probability P( overline x )
1/6
1/6
1/3
1/6
1/6
For item no. 33-40: Consider a population consisting of the values 2, 4, 6 . List all the possible samples of size n = 2 which can be drawn with replacement from the population. Describe the sampling distribution of the sample means.
33-34. Compute for the mean and variance of the population.
35-40. Find the mean, variance, and standard deviation of the sampling distribution of the sample means.
2
1
1
Sample Mean
3
5
6
7
Frequency
1
1
4
drawn from the population.
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?
