Vocab
The proportion of times an event occurs in
the long run, as a probability experiment is repeated over and over again.
What is probability?
A fair coin is tossed two times. What is the probability that the coin comes up heads at least once?
{HH, HT, TH, TT}
3 out of 4 times or 75%.
A fair coin is tossed 10 times. X = number of times
the coin comes up heads. Is this a valid binominal experiment?
Yes, because there is a pass/fail condition, a number of trials, and the events are independent of each other.
The mean of heights for women is 64” with a standard
deviation of 3”. A randomly selected woman has a height of x = 61 inches. Find and interpret the Z-Score
Z = -1, she is one SD below the mean
Find the probability of 30 people out of 50 surveyed showing up for an event
30/50 or 0.6
All the possible outcomes of a
probability experiment.
What is sample space?
Out of 3 children, what is the probability that the second child is a boy?
{BBB, BBG, BGB, BGG, GBB, GBG, GGB,
GGG}
4/8 or 50%
Five basketball players attempt a free-throw. Let X
represent the number of free-throws made. Is this a valid binomial experiment?
Yes, the players all have the same chance of making the basket and do not affect the next player.
The mean of heights for women is 64” with a standard
deviation of 3”. A randomly selected woman has a height of x = 66 inches. Find and interpret the Z-score
Z = 0.747, she is less than one SD below the mean
Find the probability of 15 people out of 50 surveyed showing up for an event
0.3
For n > 30 for a randomly
selected sample, the original sample, even if skewed or
not a normal curve, will Approximate a normal curve for n > 30.
What is the central limit theorem?
100 people are surveyed about their cars.
52 have 1 car, 34 have 2 cars, 14 have no car.
What is the probability that a randomly selected person has 1 car?
52 out of 100 or 52%
A basketball player has the opportunity to attempt 3
free-throws. If his probability of success is .67, find
the probability of making exactly 2 baskets.
0.444411 or 44.44%
The mean of heights for women is 64” with a standard
deviation of 3”. A randomly selected woman has a height of x = 70 inches. Find and interpret the z-score
Z = 2, she is two SD above the mean
Find the probability of 40 people out of 50 surveyed showing up for an event if the probability of people showing up is .49
0.999
With a probability experiment repeated more and more, the probability will equal its theoretical probability.
What is the law of large numbers?
There were 313,752 low birth weight babies
born in U.S. and 3,477,960 babies born with normal
weights. What is the probability that a baby is a low birth weight? (Total: 3,791,712)
.0827
A basketball player has the opportunity to attempt 5
free-throws. If his probability of success is .67, find
the probability of making 3 or more baskets.
Find the Z-score if the probability is 0.45
Z = -0.12566
Find the probability of 16 people out of 50 surveyed showing up for an event if the probability of people showing up is .49
.008
A numerical outcome of a probability experiment.
What is a random variable?
Find the probability that two selected cards from a
standard 52- card deck is a 4 and then a King.
(without replacement)
4/52 and 4/51
A basketball player has the opportunity to attempt 10
free-throws. If his probability of success is .67, find
the probability of making 4 or less baskets.
.0732 or 7.32%
Find the Z score if the probability is 0.89
Find the probability of 10 people out of 50 surveyed showing up for an event if the probability of people showing up is .39
.00298