A social media website currently has 1000 members. The number of people that join the website triples every month. After how man
2 answers:
You might be interested in
Answer:
a) 51.60% probability that in a given year there will be less than 21 earthquakes.
b) 49.35% probability that in a given year there will be between 18 and 23 earthquakes.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a) Find the probability that in a given year there will be less than 21 earthquakes.
This is the pvalue of Z when X = 21. So
has a pvalue of 0.5160.
So there is a 51.60% probability that in a given year there will be less than 21 earthquakes.
b) Find the probability that in a given year there will be between 18 and 23 earthquakes.
This is the pvalue of Z when X = 23 subtracted by the pvalue of Z when X = 18. So:
X = 23
has a pvalue of 0.7611
X = 18
has a pvalue of 0.2676
So there is a 0.7611 - 0.2676 = 0.4935 = 49.35% probability that in a given year there will be between 18 and 23 earthquakes.
Answer:
Step-by-step explanation:
For #2, remember that , so
Also, (a+b)(a-b), where a and b are any numbers, (a+b)(a-b)=
. Now, to simplify, or radicalize, a number with surds in the denominator, you have to multiply the denominator by its conjugate. If there is a complex number
, where a and b are any numbers, the conjugate is always
. Lets apply these rules. The conjugate of 4+6i is 4-6i, so do this:
Our answer is (28-3i)/(26)!