1. You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $425 prize, two $105 prizes, and four $25 prizes. Find your expected gain or loss. (Round your answer to two decimal places.)
2. A package delivery service divides their packages into weight classes. Suppose that packages in the 14 to 20 pound class are uniformly distributed, meaning that all weights within that class are equally likely to occur.
X = the weight of a package in the 14 to 20 pound weight class
X~U(14, 20)
1) The Picture:
2) How did we know the height of the rectangle?
3) f(x) = ___________ where ______ ≤ x ≤ _________
4) Find the probability that a package weighs between 15 and 16.5 pounds (draw the corresponding picture)
5) Find the probability that a package weighs at least 18 pounds (draw the corresponding picture)
Recall that if X ~ U(a, b): μ=a + b /2 and σ= √(b - 2)2 /12
6) Find the mean and standard deviation
7) Find the 40th percentile of package weights in this weight class (draw the corresponding picture) (hint: percentiles are area on the left)
8) Given that a package weighs at least 15 pounds, what is the probability that it weighs over 18 pounds?
9) Find P( 12≤ x ≤ 18 | x > 15)
3.A child psychologist is interested in the number of times a newborn baby's crying wakes its mother after midnight. For a group of 50 mothers, the following information was obtained. Let X = the number of times a newborn wakes its mother after midnight. For this example, x = 0, 1, 2, 3, 4, 5. It was found that 2 children didn't wake their moms at all, 11 woke her once, 23 woke her twice, 9 woke her 3 times, 4 woke mom 4 times, and 1 woke mom 5 times. Remember, P(x) = probability that X takes on a value of x
1). Create a PDF Table
2) How do you know this is a PDF?
3) How do you know this is a discrete PDF?
4.Suppose 41% of adult workers have a high school diploma but do not pursue any further education. If 20 adult workers are randomly selected, find the probability that at most 12 of them have a HS diploma but do not pursue any further education. How many adult workers do you expect to have a HS diploma but do not pursue any further education? What is the standard deviation?
How do we know this is binomial?
In words, define the random variable X:
X takes on the values:
n =
p =
q =
X ~ B( ________, ________ )
P(x ≤ 12): _________
μ = np = __________
σ = √npq = ________
5. Find if it is binomial, if not, why?
1) Treating 1000 subjects with a new weight loss pill and recording whether there is a "yes" or "no" response when asked if they lost weight.
2) Treating 1000 subjects with a new weight loss pill and recording the number of days it took each of them to lose 10 pounds.
3) Picking 10 cards randomly (without replacement) from a deck of cards and recording whether or not it is a face card.