**Task 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.

for this Task please select ID of 5 MEC students and list their name with their ID as evidence).

**AHmed 13s10134**

**Fatema 15f53654**

**Marwa 16S56484**

**HOOR 18s12545**

**Ahlam 16f54656**

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.

**Task 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.

**Task 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: (3 marks)

**The table desgine see it in the uploded file**

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.

**Task 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:

**The table desgine see it in the uploded file
**

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.

**Task 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).

**Task 6: Answer the following:**

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

**See the Table in the uplouded file**

Find the followings:

a. unknowns 𝒙 and 𝒂.

b. Standard deviation.

c. 𝑃(𝑥<5 ∪𝑥≥9).

**Task 7: 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−(𝐷3)𝜎≤𝑋≤𝜇+(𝐷3)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(13s10134), so (D=3)**if it is zero select the first digit)

**Task 8: 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.

**(Note: D is the first two digits of your MEC ID which is (13s10134)**)

**Task 9: 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.

(Note: D is the first two digits of your MEC ID wich is **(13s10134)**)

**Task 10: Answer the following:**

An automobile company is looking for fuel additives that might increase gas mileage. Without additives, their cars are known to average D mpg (miles per gallons) with a standard deviation of D/6 mpg on a road trip from Muscat to Sur. The company now asks whether a new additive increases this value. In a study, forty cars are sent on a road trip from Muscat to Sur. Suppose it turns out that the forty cars averaged 𝑥̅=(𝑫+𝟎.𝟕𝟓) mpg with the additive. Can we conclude from this result that the additive is effective?

a. With a significance level of 5%.

b. With a significance level of 1%.

(Note: D is the first two digits of your MEC ID which is **(13s10134)** )

**Answer all the question as mention above and see the aploaded file for more details..**