For what data in your professional or personal life would it be useful to construct a frequency table or histogram? If you give this some thought, you should be able to identify several sets of data.
A frequency table or a histogram are great ways of analyzing large data sets because it makes it possible to see where most of the values lie within the measurement scale. Some of the data where it might be helpful to use these means is when analyzing the age of your colleagues, height of students in a class, or the color of cups at a coffee shop.
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After using the formula for determining the value of P16 (the 16th percentile) in a data set, the result is L = 5 (this whole number was obtained without rounding). How do we use this result to determine the value of P16?
Because the top 10% occurs at the 90 th percentile for z,
The 16 th percentile occurs when,
It is common for car insurance companies to charge higher premiums for younger drivers. Younger drivers tend to earn less income than older drivers on average. So why are younger drivers expected to pay higher premiums? Do insurance companies have a right to charge different premiums to different customers for the same coverage based on their age?
Statistics show that younger drivers are inexperienced in the roads, and they are more likely to commit traffic violations or be involved in auto accidents. Car insurance companies take these aspects into consideration, and thus charge higher premiums for younger drivers.
In a simple game, a six-sided die is rolled 4 times. If all four rolls result in either 1 or 2, then the player wins $50 dollars. If the player has to pay $10 to play the game, what are the expected winnings of the player over time if many games are played?
If you roll a fair die a single time, there is a 1/3 probability of getting a 1 or a 2.
The probability of 4 consecutive wins in 4 trials, with the probability of success on a single trial is:
So, eventually you win 1 time for every 81 rounds played, and lose 80 times every 81 times you play.
When you play, you pay $10 and when win you get $50 back for a net gain of $40. When you lose, you pay $10 and get nothing back for a net gain of -$10.
Therefore, the overall profit per game is:
Thus, if you pay $10 to win $0.62, the player will lose faster than he will gain.
The scores on a particular test are normally distributed with mean of 73 and standard deviation 5. What score would a student need to be among the top 10% of all test scores?
Top 10% means the total area under a curve towards the right of a Z score, which means that the area of the left of the Z score is 90%. The Z score for 0.90 is 1.282.
Any score above 79.41 will be within the top 10%
What are the similarities and the differences between the family of t distributions and the standard normal distribution?
A normal distribution is used for a normal set and distribution of data. It is characterized by the standard deviation and mean of the data. The t distribution is used to estimate the standard error of the mean of a given dataset. A normal distribution is best for a perfectly distributed population while a t distribution is used when checking the mean of the population.
