Discrete and Continuous Variables
Determine if the following variable is a discrete, continuous, or neither:
Number of tickets sold to a randomly selected basketball game.
Discrete.
68%
Independent random variables are shown below.
S - mean=34.8 and SD=7.9
T - mean = 53 and SD=6.5
What is the mean of V if V = S+T
87.8
Over the history of the World Cup, about 70% of penalty kicks in a shootout are made. Let’s assume this is the probability for each of the players on the U.S. team and that each kick is independent. What is the probability that the team will make all 5 penalty kicks?
0.7^5 = .16807
Determine if a binomial distribution can be used to model each of the following random variables.
Rolling a fair six-sided die eight times and counting the number of rolls that land on a 5.
Yes
Determine if the following variable is a discrete, continuous, or neither:
The suit of a card randomly selected from a deck of playing cards.
Neither
What does the z-score represent?
The # of standard deviations away from the mean.
Independent random variables are shown below.
S - mean=34.8 and SD=7.9
T - mean = 53 and SD=6.5
What is the SD of V if V = S+T
SD = 10.23
Over the history of the World Cup, about 70% of penalty kicks in a shootout are made. Let’s assume this is the probability for each of the players on the U.S. team and that each kick is independent. What is the probability that the team will miss all 5 penalty kicks?
.00243
What does BINS stand for?
B - Binary
I - Independent
N - Number of trials
S - Success probability is the same
Determine if the following variable is a discrete, continuous, or neither:
The weight of a randomly selected UFC fighter.
Continuous
Check answer.
At a randomly selected department store, the mean price of a women's sweater is $33 with a SD of $9. The mean price of a randomly selected women's shirt is $16 with a SD of $5. X = the total price of a randomly selected shirt and sweater. What is the mean of a randomly selected total price?
$49
Over the history of the World Cup, about 70% of penalty kicks in a shootout are made. Let’s assume this is the probability for each of the players on the U.S. team and that each kick is independent. What is the probability that the team will make 4 total penalty kicks?
0.36015
Of the Fortune 500 companies (the top 500 US companies with the highest revenue), 10.6% are run by female CEOs . Suppose we choose a random sample of 30 companies from this list and count the number of companies in the sample that have female CEOs. Is the random variable of interest binomial with n=30 and p=0.106?
Yes, because the sample size is less than 10% of the population.
At SeaTac, the ground train shuttles passengers from one terminal to another. It departs every three minutes. Let X = time spent waiting for the train to depart for a randomly selected passenger.
Create a graph of the probability distribution of X (be sure to label axes.
Check answer -
Uniform graph, x axis is time spent waiting from 0 to 180. Y is the P(x) which is 1/180
A final exam for an AP Stats class had 60 questions. For all the students that took the exam, the mean number of questions answered correctly was 54, with a standard deviation of 12. Would it be reasonable to assume that the distribution of the number of questions answered correctly is approximately normal?
No, you can't possibly have more than 1 standard deviation away from the mean.
At a randomly selected department store, the mean price of a women's sweater is $33 with a SD of $9. The mean price of a randomly selected women's shirt is $16 with a SD of $5. X = the total price of a randomly selected shirt and sweater. What is the standard deviation of a randomly selected total price?
SD= 10.29
Dante takes the bus to school each day. It is known from past experience that the bus is late to Dante’s bus stop on 17% of days. Assuming daily bus arrivals are independent of one another, what is the probability that the bus will be late to Dante’s bus stop at least 10 times out of the 21 school days this month? Find the probability.
0.0011
Suppose that 65% of high school students eat breakfast before going to school. A random sample of 500 high school students were surveyed. Let X = the number of high school students in a random sample of size 500 who eat breakfast before going to school.
Use a BINOMIAL distribution to find the probability that 300 or fewer high school students in the sample eat breakfast before going to school.
0.011
At SeaTac, the ground train shuttles passengers from one terminal to another. It departs every three minutes. Let X = time spent waiting for the train to depart for a randomly selected passenger.
Find the probability that a randomly selected passenger waits less than 45 seconds. P(x<45)
45 * 1/180 = 0.25
On a reaction time tracking website, the distribution for reaction times is approximately normal, with a mean of 284 ms and a standard deviation of 50 ms. To be considered for a pro e-sports team, you must be in the top 1% of all reaction times. What reaction time would someone need to have on this website in order to be considered for the pro e-sports team?
167.7 milliseconds.
In a long-term study conducted in Poland, it was found that the distribution of birth weights for full-term male babies was approximately normal with a mean of 3,622 grams and a standard deviation of 432 grams. The distribution of birth weights for full-term female babies was also approximately normal with a mean of 3,465 grams and a standard deviation of 414 grams. Assuming the birth weights are independent, what is the probability that a randomly selected female baby weighs more than a randomly selected male baby at the time of birth? (Round to 4 decimal places.)
0.3965
At University A, 19% of undergraduate students have declared a major in Business, while 7% of undergraduate students at University B have declared a major in Business. A random sample of 250 students at University A and an independent random sample of 250 students at University B were selected. Assume students declare their major independently of one another. If the two samples are combined, what are the expected total number of students who have declared Business as a major and the standard deviation of the total number of students who have declared Business as a major respectively?
65 and 7.4
Suppose that 65% of high school students eat breakfast before going to school. A random sample of 500 high school students were surveyed. Let X = the number of high school students in a random sample of size 500 who eat breakfast before going to school.
Use a NORMAL distribution to find the probability that 300 or fewer high school students in the sample eat breakfast before going to school.
0.0095