1. Let X represent the change of weight a person will lose in one week when put on a special diet.  A researcher models this random variable as having a uniform distribution on the
interval [-5, 2].  Assuming this model is correct:
a) Is X a continuous or discrete random variable?
b) What's the probability a person will lose weight?
c) What's the probability that a person will lose between 0 and 3 pounds?
d) What's the probability a person will lose more than 4 pounds?
e) If infinitely many people took this diet, 10% of them would lose more than x pounds.  What's x?
f) What's the expected value and the variance of X?

2. Consider, once again, the class data.  Suppose we're randomly selecting a person from that list, and let X be the person's weight.
a) What's the pdf of X?  (Hint: X is discrete.)
b) What's the expected value of X?  How would this change if everyone held a 10-pound weight in their hand?
c) To convert weights from pounds to kilograms, multiply the weight in pounds by .4536.  What's the expected value of X in kilograms?

3. Suppose we select 5 people at random from the class list, WITH replacement.  How many men can we expect to have selected?  What's the SD for the number of men?  What's the probability we'll select4 or more men?

Postpone Number 4 until next Friday.
4. For sufficiently large values of n, the binomial pdf can be approximated by a normal distribution with mean np and variance np(1-p).  For p = .5, an n of 100 is more than enough to make this a valid approximation.  Psally the Psychic claims to be able to guess whether a coin comes up heads or tails.  She does not claim perfect accuracy, but still claims to have a "sixth sense" that helps her do this.  If she is a fraud, then she just guesses like all of us do.
a) What's the approximate probability that Psally will get 60 or more coin flips correct in 100 tosses if she is just guessing?
b) Suppose its National Psychic Day and 10,000 people all participate in this experiment in which they guess coin flips in 100 flips of a fair coin.  About how many people do we expect to get 60 or more correct?

5. A large national study found that the heights of women, age 18-24, in the U.S. were normally distributed with mean 64.3 inches and SD 2.6 inches.
a) What's the probability a randomly selected woman from this age group will be shorter than 60 inches?
b) ....taller than 70 inches?
c) To play basketball in a particular women's league, a woman must be taller than 70 inches.  Suppose we select 10 women at random (from this age group).  What's the probability that we'll have 5 or more people who can play on our basketball team?
d) What percent of women are between 65 and 75 inches tall?
e) At least how tall is a woman if  she is in the tallest 5% of the 18-24 age group?

6. The heights of men (ages 18-74) in a large national study were found to be normally distributed with mean 69 inches and SD 3 inches.
a) Suppose a man is selected randomly from thsi group, and a woman is selected randomly from the 18-24 group.  What's the expected value for the sum of their heights?
b) What's the expected value of the average of their heights?
c) What's the SD of the average of their heights?
d) What's the probability that the average height will be more than 70 inches?

7. The book, pg. 56, 2.26 AND 2.29

Postpone Number 8 Until Next Friday
8.  Let X = the number of tosses of a coin until a Head first appears.  For example, you toss a coin and get (in this order) TTH, then X=3.
a) Find the pdf of X if the probability of a head on any given toss is p and assume p < 1.  (Hint, P(X=0)=0, P(X=1) = p).  This is called the geometric distribution.
b) What's the largest possible value of X?
c) What's the expected number of tosses before a H appears?  (Hint: Look up geometric sums in your calculus book.  If it only gives you the formula for finite sums (up to n), then take the limit as n goes to infinity.  (What is the limit of p^n as n goes to infinity if 0<p <1?)