Answer:
See below.
Step-by-step explanation:
1.) 5√6
2.) 6√2
3.) 3√7
To solve this without the use of a calculator, split the given number into a series of products (numbers multiplied) and look for pairs.
Look at the attached example of Problem 1 to get a better idea of what I mean.
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis.
We can say that at 5% of significance the mean average waiting time is significantly less than 200 seconds per call.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the population mean is less than 200, the system of hypothesis are :
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a one-side left tailed test the p value would given by:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis.
We can say that at 5% of significance the mean average waiting time is significantly less than 200 seconds per call.
Answer:
There is 1.98% of probability of being dealt a flush in 5-card Poker
Step-by-step explanation:
To know the probability of a flush being dealt, we can calculate the number of cases when that happens and divide it by the total number of cases of poker hands that exist, naming A the event of a flush.
We will use combinations (nCr button on a calculator) to count the number of cases, because we don't care about the order (it is the same to be dealt a 2, 4, 6, 7 and 8 of hearts than the opposite order), being a flush the event when we take 5 cards out of 13 of the same suit, times 1 out of 4 possible suits and the total number of cases is taking 5 random cards out of 52.
That means there is about a 2% of probability of being dealt a flush.
In other words, of every 16660 plays, 33 will be, on average, a flush