Spread the Numbers!
The most commonly reported measure of spread for a data set.
Standard deviation
10C4
The distribution of X, the number of times that a fair coin lands on heads out of 10 flips.
Binomial(n=10, p=0.5)
The probability someone waits exactly 12 minutes for a bus if wait times are uniformly distributed between 0 and 30.
0
You are on a gameshow. There are 3 closed doors. Two of the doors contain goats, one door contains 1 million dollars. You choose a door at random, say door 1. The gameshow host reveals a goat behind door 2 and asks if you want to switch. To maximize your chances of winning 1 million dollars, should you switch, stay, or does it not matter?
For bell-shaped data, approximately this percentage of data falls within 2 standard deviations of the mean.
95%
The number of ways the top 3 finishers can be arranged in a race with 5 people.
60
The distribution of X, the first time a fair coin lands on heads.
Geometric(p=0.5)
The probability someone waits more than 12 minutes for a bus if wait times are uniformly distributed between 0 and 30.
0.6
Suppose Y1 and Y2 are jointly continuous with
f(y_1, y_2)=4y_1y_2
where
0\leq y_1 \leq 1, 0\leq y_2 \leq 1
what is
P(Y_1\leq \frac{1}{2}, Y_2 \geq \frac{1}{8})
0.2461
The sample mean of the following data. Include the correct symbol.
2, 4, 7, 7, 8, 9 12, 22
\overline{X}=8.875
When
P(A\cap B)=0
A and B are said to be this.
Mutually exclusive
The probability that Dr. Javier has made at least 1 typo in this review game if the number of typos has a Poisson distribution with a mean of 2 typo errors per review game.
0.8647
P(Z<1.02)
0.8461
Var(aY+b)
if
Var(Y)=\sigma^2
a^2\sigma^2
The Var(X) where X is discrete with
P(0)=0.05, P(1)=0.15, P(2)=0.25, P(3)=0.4 P(4)=0.15
Round to 1 decimal place and include the appropriate symbol.
\sigma^2=1.1
P(A\cap B)
where
P(A)=0.3, P(B)=0.4, P(A|B)=0.3
and
P(B|A) = 0.6
.12
Sampling for defectives from large lots of manufactured product yields a number of defectives, Y, that follows a binomial probability distribution with p = 0.1. If 10 products are delivered, the lot is rejected if there are more than 2 defects. What is the probability the lot is rejected?
0.0702
The probability that a certain individual takes more than 10 minutes to respond to a text message if their response time is exponentially distributed with a mean of 5 minutes.
0.1353
Suppose service times at a coffee shop have a mean of 4 minutes with a standard deviation of 2 minutes.
If we randomly select 50 people, what is the probability their average wait time exceeds 4.3 minutes?
0.1444
Suppose commercial times have an approximately bell-shaped distribution with a mean of 60 seconds and a standard deviation of 10 seconds. According to the Empirical Rule, approximately what percentage of commercials last between 50 seconds and 90 seconds?
83.85%
The probability of drawing a full house, rounded to 4 decimals.
Note: A full house is a poker hand that consists of three cards of the same rank and two cards of a different rank (ex. three queens and two nines).
0.0014
The probability that it takes you 10 people to find 3 avid fantasy readers if 15% of people are avid fantasy readers.
.0390
The CDF of Y, where
f(y)=cy, 0leq y\leq 4
If
y<0, F(y)=0
If
0\leq y \leq 4, F(y)=y^2/16
If
y>4, F(y)=1
The expected value of C, where C=10+40Y+2Y2 where Y is Exponentially distributed with a mean of 10.
900