Statistics and Probability Answers

1. Suppose the correlation coefficient between an explanatory variable (the size of a person’s home, measured in square feet) and a response variable (the amount they spend on alcohol per year, measured in US Dollars) is 0.34. If we change the units used to measure their home size from square feet to square meters, which of the following will be true? Assume 1 square foot is roughly 0.09 square meters.

A. The new correlation should be approximately R = 0.34/0.09 = 3.78
B. The new correlation should besame: R=0.34
C. The new correlation should be approximately R=0.34 x (0.09)^2 = 0.003
D. The new correlation should be R= 0.34 x 0.09 = 0.03

A courier service company has found that their delivery time of parcels are 50 minutes and variance of 25 minutes squared
What is the probability that a randomly selected parcel will take 60 minutes to deliver?

Using least-squares regression, the relationship between time spent gaming and phys. ed. grade is modelled by: (grade) = -1.8568*(hours gaming) + 95.728.

a) According to the model, a student who played video games 7 hours per week would have a grade of ___ % (round to the nearest tenth of a decimal place)

b) According to the model, a student who achieved a grade of 90% would spend ___ hours gaming per week (round to the nearest hour)

c) Describe the most plausible causal relationship between the number of hours spent gaming and a student's grade in physical education (e.g. accidental, common cause, etc.)

A students is going to graduate from a business department of a university by the end of the semester. After being interviewed at two companies he likes, he assesses that his probability of getting an offer from company A is 0.6, and his probability of getting an offer from company B is 0.45. If he believes that the probability that he will get offers from both companies is 0.35, what is the probability that he will get at least one offer from these two companies?

If the license plates in a Karachi consist of three letters followed by three numbers, what is the probability that a randomly generated plate ends in the numbers “786”? Consider that repetitions are allowed and order matters.

A University wishes to hire 4 faculty members for its newly established department. They have to select from a group of 8 Male and 7 Female applicants, all of whom are equally qualified to fill in the positions. If University selects 4 at random, what is the probability that:
a) All four will be Men
b) All four will be Women
c) Atleast one will be a Women
d) Atleast one will be a Men

A lot of 12 television sets chosen at random are defective , if 3 of the sets are chosen at random for shipment in hotel. how many defective set can they expect

Assume out of 500 people 280 are rice eater and rest are wheat eater. Can
we say the proportion of rice and wheat eater are same at 95%?

Think of some discrete random variable you observe on a regular basis. For example, it could be the (rounded) number of hours you sleep, how many gallons of gas are in your car when you get into it, how many boxes of cereal are in your house, how many days between grocery shopping, etc. (just make sure it takes only integer values). Try to list all of the possible values that this discrete random variable can take. If you can, collect some frequency data – give the relative frequency table and use this as an estimate of the probability distribution. Calculate the expected value and the standard deviation for this probability distribution. Interpret these parameters, and discuss whether they make sense based on your experience.