Answer:
a) We have the mean number of events is interval(5.3 events in 10 minutes), which constitutes the Poisson probability distribution.
b) 5.3
c) 5.3
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
a. What probability distributions' properties is this?
We have the mean number of events is interval(5.3 events in 10 minutes), which constitutes the Poisson probability distribution.
b. What is the expected value of the random variable x?
It is known that the mean number of occurrences in ten minutes is 5.3.
So the mean is 
c. What is the variance of the random variable x?
In the Poisson probability distribution, the variance is the same as the mean. So the variance is 5.3.
Answer:
70 minutes
Step-by-step explanation:
Mary can type the number of letters in 20 minutes = 6
Maggie can type the number of letters in 20 minutes = 5
Su Ying can type the number of letters in 20 minutes = 2
Working together they can type the number of letters in 20 minutes
= 6 + 5 + 2
= 13 letters
Working together they can type the number of letters in 1 minute = 
To type 45 letters time taken by them = 
= 
= 
= 69.230 ≈ 70 minutes
It will take them 70 minutes to type 45 letters.
Answer: minimum = 0.5
maximum = 9.0
first quartile = 3
median = 5.5
third quartile = 7.5
Step-by-step explanation:
The histogram is shown below and used to obtain the various information
Time (hour) (X) No of People (F) FX
0.5 19 9.5 -- minimum = 0.5
1 20 20
1.5 21 31.5
2 22 44
2.5 23 57.5
3 24 72 ----first quartile = 3
3.5 26 91
4 27 108
4.5 28 126
5 29 145
5.5 30 165 --median/ inter quartile =5.5
6 31 186
6.5 32 208
7 33 231
7.5 34 255-- third quartile = 7.5
8 35 280
8.5 36 306
9 37 333 --- maximum = 9
T=85.5 T = 507 T= 2666.82 T = TOTAL
mean = sumFX/sumF = 2666.82/507 = 5.26
Median = middle number = inter quartile =5.5 (507/2 = 253.5 = 254 and add the frequency from top = 19+20+21+ 22+ 23+ 24+26+ 27+ 28+ 29 =269
and 254 close to 269 that is the frequency is within the range and corresponds to 5.5
first quartile = 1/4 *507 = 126.75 = 127 ( add the frequency from top= 19+20+21+ 22+ 23+ 24= 129 and 127 is close to 129)
third quartile = 3/4 * 507 = 380.25 ( add the frequency from top = 19+20+21+ 22+ 23+ 24+26+ 27+ 28+ 29+ 30+ 31+32+ 33+ 34 = 399 and 380 is close to 399 so the third quartile is 7.5
minimum is the one with lowest frequency = 0.5 at 19
maximum or mode is the one with highest frequency = 9 at 37
Arcs get their angle measurement from the central angle they're in.
this one, has a central angle of 125°, thus the Arc is likewise the same 125°.
