Exam II

126 points total.

(5 points) Define "random variable"

Answer: A variable that assumes a numerical value associated with the outcome of an experiment.
(5 points) The sample median is more robust than the sample mean. What does this mean?

Answer: When a few observations in a dataset are changed the mean will change more than the median.
(6 points) As part of a psychology experiment a child's temperament was rated on a scale of 1 to 5 with 1 being easy going and 5 being very hard to please. This rating is:

Answer: qualitative and ordinal
(10 points) Which of the following are valid probabilities:
1. 0.5
2. 0
3. 100
4. -0.5
5. 1.38
Answer: a) and b)
Use the following table to answer these questions:

   x   |  10    15    20    25
-----------------------------------
  p(x) | 0.25  0.50  0.15  0.10

(5 points) Is this a valid discrete probability distribution? Why or why not?

Answer: Yes because the probabilities add to one and all probabilities are between 0 and 1.

(5 points) What is P(X 25)?

Answer: 1

Use the following data for these questions:

4, 5, 8, 7

(5 points) Find the sample mean

Answer: 6

(10 points) Find the sample variance and standard deviation

Answer: 10/3 and 1.83

(5 points) Find the median

Answer: 6

Hundreds of diodes (an electrical device) manufactured at a certain plant were tested to see how long they would work. Hours before failure was recorded for each diode. This data was strongly right skewed.
1. (5 points) Is the mean of this dataset larger or smaller than the median? (Or do you not have enough information to determine this?)
  
  Answer: the mean is larger since the distribution is right skewed
2. (5 points) Sketch a histogram that demonstrates what the term "right skewed" means.
3. (5 points) The interquartile range of this data was (12.5, 75.25). What percent of the data fell within this range?
  
  Answer: 50%, that is part of the definition of the inter-quartile range
Use the standard normal table to find the following probabilities (remember to draw the pictures):
1. (5 points) P(Z = 1.5)
  
  Answer: 0
2. (5 points) P(Z > 1.5)
  
  Answer: 0.0668
3. (5 points) P(-1.5 < Z < -1)
  
  Answer: 0.1587 - 0.0668 = 0.0919
4. (5 points) P(5 < X < 15) when = 10 and = 25.
  
  Answer:
  
  P(5 < X < 15) =
  P[(5 - 10)/5 < Z < (15 - 10)/5) =
  P(-1 < Z < 1) =
  1 - 2*0.1587 =
  0.6826
Use the binomial tables to find the following probabilities
1. (5 points) P(X = 2 | n = 5, p = 0.8)
  
  Answer: 0.051
2. (5 points) P(X < 2 | n = 5, p = 0.8)
  
  Answer: 0.007
3. (5 points) P(X 2 | n = 5, p = 0.8)
  
  Answer: 0.058
4. (5 points) P(0.4 < < 0.8 | n = 5, p = 0.8)
  
  Answer:
  
  P(0.4 < < 0.8 | n = 5, p = 0.8) =
  P(2 < X < 4 | n = 5, p = 0.8) =
  0.205
Use the following relative frequency histogram to answer these questions.
1. (5 points) What percent of the data had a death rate below 10?
  
  Answer: 0.05 + 0.25 = 0.30
2. (5 points) What percent of the data had a death rate between 15 and 20?
  
  Answer: 0.20
3. (5 points) What measurement class did most of the data belong to?
  
  Answer: 10 - 15