Probability
The weather app predicts that the day will have a 30% chance of rain, 40% chance of snow, and partly cloudy the rest of the day. What is the sample space for this situation?
Rain, snow, partly cloudy
An animal shelter finds that the average length of time before a dog gets adopted is 3 months. A sample of 30 dogs from this shelter is taken and are found to have an average of 2.6 months in the shelter before being adopted.
Identify the parameter and the statistic.
Parameter: 3 months
Statistic: 2.6 months
A sample of 40 test scores are found to have an average of 72.5. The standard deviation of the population is 4.2. Find the standard deviation of the sampling distribution.
0.664
What is the critical value for a 90% confidence level?
1.645
What is the notation to represent the probability that a random variable is at least 12?
P(X>=12)
A class is given a 100 question test and each question is worth 1 point. Scores are calculated and no partial credit is given for missed questions.
Are test scores a discrete or continuous variable?
Discrete
Give the notation that represents a sampling distribution taken from 65 subjects with mean of 52 of and a population standard deviation of 3.6.
N(52, 0.447)
Interpret a 95% confidence interval of (12.4, 17.2)
We are 95% confident that the true population mean is between 12.4 and 17.2
You are rolling two 4-sided dice. What is the probability that the sum is 3 or 6?
5/16 or 0.3125
Families are comparing how long it takes their children to brush their teeth.
Is time to brush teeth a continuous or discrete random variable?
Continuous
A population is found to have a right skew distribution. A sample of 100 is taken from the population. What is the shape of the sampling distribution?
Approximately normal
Calculate a 96% confidence interval for a sample size of 30 that has a mean of 53.4 and population standard deviation of 5.2.
(51.45, 53.35)
The more trials you have, the closer an event gets to its theoretical probability.
The time it takes for students to drive to school is found to have a uniform distribution between 10 and 21 minutes. What is the probability that a student will take either between 10 and 12 minutes or more than 17 minutes to get to school?
0.545
Define the Central Limit Theorem.
If the sample size is large (at least 30), then the sampling distribution will be approximately normal.
What happens to a confidence interval if a higher level of confidence is used?
The confidence interval increases
A spinner gives the following probabilities:
Red: 1/12, Yellow: 1/6, Green: 1/4, Blue: 1/2
Is this a valid probability model? Why?
Yes, all probabilities add to 1
The time it takes students to get to school is found to have a normal distribution with mean of 12 minutes and standard deviation of 2.2 minutes. What is the probability that a student will take more than 15 minutes to get to school?
0.0869
A sample of 100 test scores people is taken and found to have a mean of 78.7. The population standard deviation is 14.62. What is the probability that a score in the sample is less than 75?
0.0057
What happens to a margin of error and confidence interval when the sample size increases?
The margin of error decreases, so the confidence interval decreases