Probabilities
If P(A)= 0.4 and P(B)= 0.6, what is P(A and B)?
P(A and B) = 0.24
The number of apples in a basket are an example of a ___ random variable
Discrete
Thirty-one percent of adults say baseball is their favorite sport. A random sample of 12 persons is selected.
Describe the distribution
X ~ B(12,0.31)
Assume that length of skateboards follow a normal curve with a mean of 24 inches and a standard deviation of 5.1 inches.
Describe the distribution
X ~ N(24,5.1)
What is the z-score for the lowest 12% on an inverse normal curve?
z = -1.17
If P(A) = 0.30 and P(B) = 0.20, what is P(A or B) if A and B are independent?
P(A or B) = 0.44
P(A or B) = (0.30 + 0.20) - (0.3 x 0.2)
Give an example of a continuous random variable
Height, weight, income, time, etc.
List the 4 properties of the binomial
1. has a fixed number of trials
2. Trials are independent and sample is smaller than 10% of the population
3. two possible outcome for each trial
4. Probability of successes is p and the probability of failure is the compliment (q = 1-p)
Assume that length of skateboards follow a normal curve with a mean of 24 inches and a standard deviation of 5.1 inches.
What is the probability that a skateboard is shorter than 14 inches?
0.024952
The distribution of shoe sizes is normal with a mean of 8 inches and a standard deviation of 2.2 inches.
What is the shoe size at which 12% of the population wears a shoe smaller than this size?
5.415
Suppose the probability that a student at SDSU has a Tiktok account is 0.43 (event A) and the probability they have an Instagram account is 0.89 (event B).
Given that a student has an Tiktok account what is the probability that they have an Instagram account
0.9070
P(B/A) = P(AnB)/P(A) = 0.39/0.43
x 0 1 2 3 4
p(x) 0.07 0.20 0.38 x 0.13
solve for x = 3
x = 0.22
Thirty-one percent of adults say baseball is their favorite sport. A random sample of 12 persons is selected.
What is the probability exactly four of the twelve people say baseball is their favorite sport?
0.2349
Assume that length of skateboards follow a normal curve with a mean of 24 inches and a standard deviation of 5.1 inches.
What is the probability that a skateboard is longer 25 inches?
0.4223
The distribution of shoe sizes is normal with a mean of 8 inches and a standard deviation of 2.2 inches.
What is the shoe size at which 34% of the population wears a shoe larger than this size?
8.9075
Assume we know that the probability a person has hazel eyes is 0.30. Four people are selected at random. What is the probability that at least one of them has blue eyes?
0.7599
1-P(none) = 1 - 0.74 = 0.7599
x 0 1 2 3 4
p(x) 0.07 0.20 0.38 0.22 0.13
probability that p(x) is two or more?
p(x < 2) = 0.73
Thirty-one percent of adults say baseball is their favorite sport. A random sample of 12 persons is selected.
What is the probability that at least two of the 12 persons say baseball is their favorite sport?
0.9256
Assume that length of skateboards follow a normal curve with a mean of 24 inches and a standard deviation of 5.1 inches.
What is the probability that a skateboard is between 11 and 19 inches long?
0.1580
The distribution of shoe sizes is normal with a mean of 8 inches and a standard deviation of 2.2 inches.
Which two shoe sizes make up the middle 80%?
5.1805 and 10.8194
In a group of 20 people there are 4 with red hair, 7 with blond hair, and 9 with brunette hair. Two people are randomly selected without replacement. What is the probability that both people selected have red hair?
0.0316
(4/20)(3/19) = 0.316
x 0 1 2 3 4
p(x) 0.07 0.20 0.38 0.22 0.13
Find the expected value (mean) and standard deviation
mean = 2.14
standard deviation = 1.0956
Thirty-one percent of adults say baseball is their favorite sport. A random sample of 12 persons is selected.
What is the mean and standard deviation?
mean = 3.72
SD = 1.6021
Assume that length of baseball bats follows a normal curve with a mean of 28 inches and a standard deviation of 6.2 inches.
What is the probability that a bat is between 31 and 32 inches?
0.05483
In an inverse normal model draw a picture of the middle 60% and state the upper limit and lower limit values
-0.8416
0.8416