1. If = 5.2 and = 0.34 in a distribution of how many hours of TV people watch per week, what is the probability that a given case will fall between: (a) 4.18 and 6.22? (b) 4.52 and 5.88? 2. In a...

Probability Questions:
1. In this distribution = 5.2 and = 0.34. Assuming the distribution to be normal, the required probabilities are given below.

2. Let us consider a random variable X defined by the number of friends college students have on Facebook. Hence by the problem, . We need to find the required probabilities given below. We use the following property that for both the problems. Where μ and σ are the mean and standard deviation of the corresponding normal distribution respectively. Where the last probabilities are found from the z-table.
a)
b)
3. There are 10 true-false questions in total and for each question, there is one correct answer. So, if X denotes the number of correct questions answered, then i.e., Binomial distribution with success probability p or probability of getting a correct answer.
a) In this case, since the answering is dependent entirely on guessing, one can say that the probability of getting a correct answer is 0.5. Hence here p = 0.5. Thus the required probabilities of getting exactly 5 questions correct is given below.
b) By the problem, it is assumed that after being reasonably well prepared I have been able to answer 80% of questions correctly on various tests and hence the probability of getting the correct answer has now been increased to 0.8 or p can be taken as 0.8. Thus the required probability of getting at least 9 questions right is given below.

4. Here 50 applicants are applying for three posts available in the university with an equal capability and 20% of them or 10 applicants are minorities. All their application folders have been scrambled and stacked on top of each other. The first position can be arranged in 50 ways. Similarly, the second position of the stack can be arranged in 49 ways and the third position can be arranged in 48 ways. Thus the first three positions can be arranged in 50*49*48 ways. The first three applications on the top of the stack are the selected ones to join as three new Associate Deans.
a) If 3 minorities are to be selected then the first three positions of the stack from the top should be the minorities application folders. So, a minority application folder can be placed in the first position of the stack in 10 ways. The second minority position being in the second place can be done in 9 ways and lastly, the third position being another minority folder can be done in 8 ways. Thus the required probability for the selection of three minorities is given by
b) Now, the probability of selecting at least one minority is equivalent to the following.
. Hence the first position can be filled by anyone of the 40 other applicants. The second position can be filled in 39 ways and lastly, the third position can be...