Reference no: EM132559124

MASC-B 1001 Business Mathematics and Statistics - Middle East College

Learning Outcome 1: Calculate probabilities of different types of events.

Learning Outcome 2: Compute probabilities using discrete probability distributions and continuous probability distributions.

Assignment Objective

To assess learning emphasized on basic concepts of probability and probability distribution, problem solving skills and the ability to apply this knowledge in Business.

Question 1: Answer the following:

Consider a box contains cards with your ID number and 5 another student's ID (i.e. each card will contain either a number or a letter). Answer the following:

a. If one card is selected at random.
i. Find the probability that the selected card contains a number.
ii. Find the probability that the selected card contains a letter.

b. If two cards are selected at random one after another. What is the probability that both cards contain a letter? If each card is
i. Replaced.
ii. Not replaced.

Question 2: Answer the following:
Make a short survey among 40 people of "Do you support a partial curfew from (6 pm until 6 am) to curb some irresponsible behavior in society?" (Remark: use google form/email /Kaizala
/Twitter to distribute the survey and take a screenshot of your work). Based on your result.
a. Calculate the probability of persons who support a partial curfew.
b. Calculate the probability of persons who do not support a partial curfew.

Question 3: Answer the following:

As is the case around the world, we in Oman too are confronted with the unprecedented challenges posed by the COVID-19 (Corona Virus) pandemic. Therefore, the teaching moved to online platforms, but some students dislike the online learning for many reasons. Make a short survey among 30 students (male and female) of "Do you prefer online learning or face-to-face learning" and take a screenshot of your work. Fill your result in the following table:

Based on your result. One student selected at random, find the probability that.

a. The student does prefer online learning given that he is a male.
b. The student prefers face-to-face learning, or she is female.
c. The student either male or prefer face-to face learning.

Question 4: Answer the following:

Each student should select three different states from different regions in Oman about the cases of infection and recovering taken from the Supreme Committee about the spread of Coronavirus (COVID-19) in a particular day. (Remark: take a screenshot as evidence). Then obtained your result in the following table:

Based on the result, find the probability that the selected person is:

a. from state B or he is recovered.
b. recovered given that he is from state C.
c. from state B given that he is infected.
d. infected or from state A.

Question 5: Answer the following:

Waleed decided to construct a probability distribution of tossing five coins. He considers his random variable X, to be the number of Tails on all five coins.
a. List the sample space for the experiment.
b. What are the possible values for X?
c. Construct a probability distribution for his experiment.
d. Find E(-4x + 16).
e. Find V(-6x).

Question 6: Answer the following:

If the following table represent a probability distribution with an expected value of 9.

Find the followings:

a. unknowns x and a.
b. Standard deviation.
c. P(x < 5 U x ≥ 9).

Question 7: Answer the following:

A traffic cop has been determined that (D %) of drivers checked use their mobile phones and ((D+6) %) of drivers checked do not wear seat belts. In addition, it has been observed that the two infractions are independent from one another. If the cop stops seven drivers at random:
a. Calculate the probability that exactly five of the drivers have committed any one of the two offenses.
b. Calculate the probability that at least one of the drivers checked has committed at least one of the two offenses.

Question 8: Answer the following:
The life span of 100 W light bulbs manufactured by a company are tested. It is found that of the light bulbs are rejected. A random sample of 15 bulbs is taken from stock and tested. The random variable X is the number of bulbs that is rejected.
a. Give four reasons why X will have a binomial distribution.
b. Use a formula to find the probability that 2 light bulbs in the sample are rejected.
c. If the true probability of a rejected light bulb is 0.5340. Among the next 6 randomly selected bulbs, what is the probability that at least one of them is accepted?

d. If life span of light bulbs is adjusted so that the mean now is ρ. Find the value of ρ:
i. Given that P(X = 0) = 0.25.
ii. Given that the variance of X is 2.4.
(Note: D is the second digit of your MEC ID, if it is zero select the first digit)

Question 9: Answer the following:
1. If the weight of the students expressed by X"a random variable" with a distribution of N(μ, σ), find: P(μ - (D) σ ≤ X ≤ μ + (D) σ).

2. It assumed that the maximum temperature in Oman is normally distributed with a mean of D and a standard deviation of D/2 for which: P(D - a ≤ X ≤ D + a) = 0.5934. calculate the value of "a ".
(Note: D is the second digit of your MEC ID, if it is zero select the first digit) Question 10: Answer the following:
The profits of a mobile company are normally distributed with Mean of R.O (D x 10) and standard deviation of R.O (D).

a. Find the probability that a randomly selected mobile has a profit greater than R.O ((Dx10) +10).

b. Any mobile phone which profit is greater than R.O ((Dx10) +10) is defined as expensive. Find the probability that a randomly selected mobile has a profit greater than R.O ((Dx10) +20) given that it is expensive.

c. Half of expensive mobile phones have a profit greater than R.O h. Find the value of h.

Question 11: Answer the following:

The weight, in kilograms, of cereal in a box can be modelled by a normal distribution with Mean μ and standard deviation 5.4 kg. Given that 10% of boxes contains less than D kg. Find.

a. The value of μ.

b. The percentage of boxes that contain more than (D+4) kg.

c. If the machine settings are adjusted so that the weight of cereal in a box is normally distributed with mean (D+3) kg and standard deviation of σ. Given that the probability of boxes contains between D kg and (D+6) kg is 0.9671, find the value of σ.

Attachment:- Business Mathematics and Statistics.rar