Probability
Discrete Random Variables
Normal Distributions
Sampling Distributions
Miscellaneous Math
100
When rolling 1 fair die, what is the probability of rolling a number larger than 4?
2/6=1/3
100
Using the table, find
P(X=5)
0.20
100
What is the area to the left of a z-score of 1.42?
.9222
100
How does the mean of a sampling distribution relate to the mean of a population?
They are the same
100
Give an example of two data sets that have the same mean, median, and mode, but are not identical.
A: 1,2,3,3,4,5
B:0,1,3,3,5,6
200
When rolling two fair dice, what is the probability of rolling a sum of 5?
4/36=1/9
200
Using the table, find
P(X>6)
0.65
200
What is the area to the right of a z-score of -0.53?
.7019
200
If a population has a mean of 15, and a standard deviation of 2, then what would the mean and standard deviation be for the sampling distribution if
n=36
Mean = 15
Standard Deviation =
0.bar3
200
What measure of center is most sensitive to the presence of outliers? What measure of center can be used for qualitative data?
Mean; Mode
300
When rolling two fair dice, what is the probability of rolling a sum of 6 or doubles?
10/36=5/18
300
Calculate the expected value of the table
7.42
300
A study found that the mean systolic blood pressure was 105 mm Hg. Assume that systolic blood pressure follows a normal distribution with μ=105 and σ=8. Find
P(102<x<109)
.3395
300
Which distribution can not be analyzed?
A) Normal,
mu=4, sigma=1, n=55
B) Left-Skewed,
mu=40, sigma=10, n=20
C) Unknown,
mu=1, sigma=1, n=100
D) Normal,
mu=86, sigma=75, n=309
B
300
What is the IQR of the following data set:
80, 75, 84, 78, 77, 78, 78, 68, 78, 87, 80, 84
4.5
400
When rolling three fair dice, what is the probability of rolling triples?
6/216=1/36
400
According to the National Center for Education Statistics, 20% of students at Harvard University are Asian-Americans. A random sample of 15 students is taken. Find the probability that exactly 3 students in the sample are Asian-American.
binompdf(15, .20, 3) = .25
400
A study found that the mean systolic blood pressure was 105 mm Hg. Assume that systolic blood pressure follows a normal distribution with μ=105 and σ=8. What blood pressure represents the 15th percentile?
96.68
400
The breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 500 psi. What is the probability that the sample mean breaking strength for a random sample of 64 rivets is between 9,950 and 10,050?
.5762
400
A U.S. Army drill instructor will perform inspection on 2 soldiers in a squad of 30 soldiers. If both soldiers fail the inspection because their rifles are not clean, the entire squad will have to run a five-mile course in full gear. 5 of the 30 soldiers have rifles that are not clean. What is the probability that the squad will have to run the course?
0.0229
500
When rolling two fair dice, what is the probability of rolling a sum of 6, given both of the dice are even?
2/9
500
According to the National Center for Education Statistics, 20% of students at Harvard University are Asian-Americans. A random sample of 15 students is taken. Find the probability that at least 2 of the students in the sample are Asian-American.
1 - binomcdf(15,.20,1) = .83
500
In a normal distribution where the mean is 100, a raw score of 104.1125 represents the 95th percentile. What raw score represents the 99th percentile? (Round to the nearest hundredth)
105.825
500
The loan amounts of a large lender have a standard deviation of $15.37 million. What is the probability that a sample of 200 loans will have a mean within 1 million of the actual mean?
.6424
500
Lenny went to the church bazaar with his family. At the bazaar there is a game involving two dice. You can pay $1 to play the game, and you get two rolls of the dice. If you roll a sum of 7 one time you get $5 back, and if you roll a sum of 7 twice you get $12 back. What is the expected value of the game as a player?
$0.72