Normal Distributions
The mean score of a test is 75 with a standard deviation of 6. Random samples of size 40 are drawn from this population and the mean of each sample is determined. Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution.
mean = 75
standard error = .9487
If the average height of a kindergartner is 3.2' with a standard deviation of .6', what is the probability that I find a kindergartener that is between 3' and 3.4' tall?
.2611
If the mean SAT score is 1100, with a standard deviation of 25, what score is the 75th percentile?
1117
A manufacturer produces light bulbs with a mean lifespan of 800 hours and a standard deviation of 50 hours. If a random sample of 36 light bulbs is taken, what is the probability that the sample mean lifespan will be less than 790 hours?
.1151
In a multiple-choice test with 10 questions, each having 4 answer choices, what is the probability that a student who guesses randomly will answer exactly 3 questions correctly?
.2503
What is the z-score formula?
z = x-mean / standard deviation
If a bag of candy weighs 8 pounds, with a standard deviation of 1.5 pounds, What is the probability I find a bag of candy that weighs less than 7.2 pounds?
.2969
In a city, the average commute time to work is 30 minutes, with a standard deviation of 5 minutes, following a normal distribution. What is the maximum commute time within which the fastest 20% of the commuters fall?
34
In a factory, the weight of a product follows a normal distribution with a mean of 200 grams and a standard deviation of 30 grams. If you randomly select 16 products, what is the probability that the sample mean weight is less than 195 grams?
.2533
What is the probability of selecting two 7's from a deck of cards?
.0045
What is the mean and standard deviation of a z score?
mean = 0
standard deviation = 1
What is the probability I find a student with a GPA of at least 3.8, where the class has an average of 3.4 and a standard deviation of .2?
.0228
The mean score on a standardized test is 100, with a standard deviation of 15. What is the minimum score needed to be in the top 10% of test-takers?
119
The exam scores in a large class have a mean of 70 and a standard deviation of 15. If you randomly select 100 exams, what is the probability that the sample mean score is greater than 72?
.9082
If the odds of a kid getting a full-sized candy bar are 1 in 15 houses, what is the probability, that they get their first full-size bar on the 5th house?
.0506
Which direction is the cumulative area?
Left
What is the probability that one of my students will score at most 1200 on the SAT, when the average is 1100, with a standard deviation of 50?
.9772
The average waiting time for customers at a bank is 15 minutes, with a standard deviation of 3 minutes, following a normal distribution. If the bank wants to serve 90% of customers within what waiting time, what is the maximum waiting time they should target?
20
A smartphone manufacturer's battery life follows a Weibull distribution with a mean of 48 hours and a standard deviation of 12 hours. If you randomly select 49 smartphones, what is the probability that the sample mean battery life is greater than 50 hours?
.8789
What is your favorite subject?
It better be math :)
Does a taller graph (normal curve) have a larger or smaller standard deviation?
smaller
If there are 56 people in the senior class, how many of them will have a GPA of more than 3.2, if the class average is 3.0, with a standard deviation of .4?
17
The average temperature in a city during summer is 85°F with a standard deviation of 10°F, following a normal distribution. If you want to be in the top 15% of the coolest summer days, what is the highest temperature you should expect?
75
The average time it takes for customers to complete a certain task is 12 minutes, with a standard deviation of 2 minutes. If you randomly select 25 customers, what is the probability that the sample mean completion time is less than 11 minutes?
.0062
In a deck of 52 playing cards, a player draws 5 cards at random with replacement. What is the probability that the player gets at least one Ace in the 5 cards drawn?
.3298