Probability
Counting Methods
Discrete Probability Distributions
Normal Probability Distributions
Confidence Intervals
100
If the probability of a student passing a certification exam is 0.72, what is the probability of the complement?
P(not passing)=0.28
100
A customizable laptop offers 3 processor speeds, 4 RAM sizes, and 2 hard drive options. How many different laptop configurations are possible?
24 laptop configurations
100
State the three requirements for a potential probability distribution to be considered valid.
1. There must be a numerical random variable x.
2. Each probability must be valid. 0<=P<=1
3. The sum of the probabilities must equal 1.
100
What is the total area under a standard normal distribution curve, and what is its mean and standard deviation?
area=1
mu=0
sigma=1
100
If a 95% confidence interval for a population mean is found to be (45.2, 54.8), what is the best point estimate and margin of error?
\bar{x} = (45.2 + 54.8)/2 =50
E=(54.8-45.2)/2=4.8
200
A bag contains 8 red marbles, 5 blue marbles, and 7 green marbles. If one marble is randomly selected, what is the probability it is blue OR green?
P(Blue or Green) = 3/5 or 0.6
200
A club with 15 members needs to choose a President, Vice President, Secretary, and a Treasurer. How many different ways can these positions be filled?
15P4 or 15 xx14xx13xx12=32,760
200
If 20% of all smart bulbs are defective, find the probability that in a random sample of 6 bulbs, exactly 2 are defective. Round to three decimal places.
binompdf(6, 0.20, 2)=0.246
200
A company produces light bulbs with a mean life of 1,000 hours and a standard deviation of 50 hours. If the life spans are normally distributed, what percentage of light bulbs will last between 920 and 1,050 hours? Round to three decimal places.
P(920<x<1050)= normalcdf(920, 1050, 1000, 50)=78.655%
200
What is a confidence interval used for?
To use sample data to estimate a range where a population parameter is likely to be.
300
Using the table provided, if one order is randomly selected, find the probability that it is Incorrect, given that the order came from Starbucks. Round to three decimal places.
P(incorrect|Starbucks)=35/280=0.125
300
A quality control inspector must randomly select 4 microchips to test from a batch of 20. How many different groups of 4 microchips can be selected?
20C4=4,845
300
The following table describes the probability distribution for the number of pets x owned by households in a specific neighborhood. Find the mean and the standard deviation for this distribution. Round your final answers to two decimal places and include proper notation.
mu=1.15
sigma=0.91
300
The weights of apples in an orchard are normally distributed with a mean weight of 150 g and a standard deviation of 20 g. Find the probability that a randomly selected apple weighs more than 180g. Round to three decimal places.
P(x > 180)=normalcdf(180, 999999, 150, 20)=0.067
300
A social media company is investigating how many of its users have "dark mode" enabled. In a random sample of 600 users, the company finds that 432 of them use dark mode. Construct a 95% confidence interval for the proportion of all users who prefer dark mode. Round to three decimal places. Interpret the interval.
0.684<p<0.756
We are 95% confident that between 68.4% and 75.6% of all users on this social media platform use dark mode.
400
Two cards are drawn from a standard 52-card deck without replacement. Find the probability that both cards are Aces. Round to three decimal places.
P(ace and ace)=
4/52 xx 3/51 = 0.004
400
A university is creating new student ID codes. Each code must consist of two letters followed by three digits. To avoid confusion, the letters I, O, and Q cannot be used, and the first digit of the three-digit sequence cannot be zero. How many unique ID codes can be created?
23xx23xx9xx10xx10=476,100
400
A survey finds that 40% of adults prefer dark roast coffee. If a random sample of 50 adults is selected, find the mean and standard deviation for the number of people who prefer dark roast. Round to two decimal places.
mu=20
sigma=3.46
400
A study finds that adult heights are normally distributed with a mean of 67" and a standard deviation of 3". Find the height that separates the top 10% of adults from the rest. Round to one decimal place.
x=70.8"
400
A sample of 25 test scores has a mean of 75 and a standard deviation of 10. Construct a 90% confidence interval for the population mean. Round to two decimal places. Interpret the interval.
71.58<mu<78.42
We are 90% confident the mean test score for all test takers is between 71.58 and 78.42.
500
Bank of America requires a 6 digit pin number (digits 0-9) for a debit card. Digits can be used more than once. A stranger is trying to guess your pin. What is the probability that they get it correct on the first guess? Leave your answer as a fraction.
P(correct)=1/(1,000,000
500
At Hogwarts School of Witchcraft and Wizardry, the Sorting Hat chooses one of four houses for each first-year student. If 4 students are randomly selected from 16 available students (including Harry Potter), what is the probability that they are the four youngest students? Leave your answer as a fraction.
P(youngest)= 1/(16C4)=1/(1,820)
500
According to a survey, 65% of households own a pet. In a sample of 20 households, find the probability that at least 13 own a pet. Round to three decimal places.
1-binomcdf(20,0.65,12)=0.601
500
The mean score on a math exam is 80 with sigma=12. If a random sample of 36 students is tested, find the probability that their mean score is between 78 and 82. Round to three decimal places.
P(78<x<82)= normalcdf (78, 82, 80, 12/sqrt36)=0.683
500
A nutritionist is measuring the sugar content in a specific brand of cereal. A random sample of 16 boxes results in a sample standard deviation of 1.2 grams. Construct a 95% confidence interval for the true population standard deviation of the sugar content. Round to two decimal places. Interpret the interval.
\chi^2 R: 27.488
\chi^2 L: 6.262
0.89 < \sigma < 1.86
We are 95% confident the standard deviation of the sugar content in all boxes of this brand of cereal is between 0.89 and 1.86 g.