A California licence plate consists of a sequence of seven symbols: number, letter, letter, letter, number, number, number, wher
1 answer:
Answer:
There is a 44.73% probability that all symbols are different.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
There are 26 total letters and 10 total digits.
The plate has the following format:
number, letter, letter, letter, number, number, number
Total outcomes
Each number can have 10 values.
Each letter can have 26 values.
There are four numbers and 3 letters.
So there are
possible plates
Desired outcomes
We cannot have repeated values.
So, for example, the first number can be any of the 10 digits. The second can be any of them, bar the first one. So 9 possible digits
The same logic for the letters, 26, then 25, then 24.
So there are
10*26*25*24*9*8*7 = 78624000 plates in which all symbols are different.
(a) What is the probability that all symbols are different
There is a 44.73% probability that all symbols are different.
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Answer:
(2)
(3)
The mean calculated for this case is
The sample deviation calculated
So on this case the 99% confidence interval would be given by (3.896;21.704)
Step-by-step explanation:
Data: 10,9,20,13,12
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
The mean calculated for this case is
The sample deviation calculated
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,4)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (3.896;21.704)