A bakery opens every day from Monday to Saturday, but only in the morning
on Wednesdays. It is known that the number of bread rolls sold daily follows
a Gaussian distribution with mean 130 and standard deviation 20 with the
exception of Wednesdays for which the distribution of the number of bread
rolls sold is still Gaussian but with mean 100 and standard deviation 30.
(a) What is the probability that on a Wednesday the bakery will sell more
than 140 bread rolls?
(b) What is the probability that on a random opening day the bakery will
sell more than 140 bread rolls?
(c) What is the probability that in a week the bakery will sell more than
800 bread rolls?

Distillation postlab questions

1.)As a liquid begins to distill, a student notes that the boiling chips are missing. The student removes the thermometer and drops a few chips into the distillation flask. What will probably happen? What is the correct procedure?

2.)Why is better separation of two liquids achieved by a slow rather than a fast fractional distillation?

A researcher is studying immune response in mice. He removes the thymus from each mouse surgically when it is born to study the effect on immune cell maturation. Later, when he gives the mice a vaccine, he finds that they produce few or no antibodies in response to this immune challenge. Explain how the lack of a thymus led to this result.

You are tossing a coin and it has a probability of p to show heads on any given toss. You keep on tossing the coin until you see a heads. Let X represent the number of tosses until you see a heads.

1. Find the probability that X is odd.
2. Find the probability that X is even, DO NOT USE QUESTION 1.
3. Let's say the coin is balanced, what is the probability that X is odd? Is this contrary to intuition?

Suppose it is known that the probability of being susceptible to contract a seasonal flu disease in a town is 0.20. A bio-statistician randomly selected 12 unrelated people from the town and examined if they are susceptible to the disease. Considering upto 4 decimal places, find the following: (a) expected number of susceptible individuals; (b) probability that 2 or fewer susceptible individuals; (c) probability that exactly 3 susceptible individuals; (d) probability that at least 4 susceptible individuals.

In a large corporation, 65% of the employees are male. A random sample of 5 employees is

selected. We wish to determine the probability of selecting exactly 3 males. Use an appropriate

probability distribution to answer the following:

(a) Define the variable of interest for this scenario.

(b) What is the probability that the sample contains exactly three male employees?

(c) Justify the suitability of the probability distribution that you used to solve part (a).

(d) What is the expected number of male employees in the sample?

In a large corporation, 65% of the employees are male. A random sample of 5 employees is selected. We wish to determine the probability of selecting exactly 3 males. Use an appropriate probability distribution to answer the following:

(a) Define the variable of interest for this scenario.

(b) What is the probability that the sample contains exactly three male employees?

(c) Justify the suitability of the probability distribution that you used to solve part (a).

(d) What is the expected number of male employees in the sample?

1. Rolling doubles When rolling two fair, 6-sided dice, the probability of rolling doubles is 1/6. Suppose Elias rolls the dice 4 times. Let W = the number of times he rolls doubles. The probability distribution of W is shown here. Find the probability that Elias rolls doubles more than twice.

a.

b.

Assume the online test in HA1011 has 15 multiple questions. Each question has five possible answers, of which only one is correct.

1. What is the probability that guesswork will yield at least seven correct answers?

2. What is the expected number of correct answers by guesswork?

At Delta limited the Chief Administrative Manager analyzed the number of incoming faxes. After an analysis, the manager determined the probability distribution of the number of pages per fax as follows:

Required:
Compute the mean and the variance of the number of pages per fax.

A manager at a company that manufactures cell phones has noticed that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of one​ day's run seems to have no bearing on the next day.

Question:

​a) What model might you use to model the number of faulty cell phones produced in one​ day?

​b) If the mean number of faulty cell phones is 3.4 per​ day, what is the probability that no faulty cell phones will be produced​ tomorrow?

​c) If the mean number of faulty cell phones is 3.4 per​ day, what is the probability that 3 or more faulty cell phones were produced in​ today's run?