Answer:
x |
f |
f*x |
0 |
14 |
0 |
1 |
31 |
31 |
2 |
47 |
94 |
3 |
41 |
123 |
4 |
29 |
116 |
5 |
21 |
105 |
6 |
10 |
60 |
7 |
5 |
35 |
8 |
2 |
16 |
Total |
200 |
580 |
mean = 580/200=2.9 |
λ= 2.9
P(X=x) = e-λ λx / x! for x = 0, 1, ....8
P(X = 0) = 0.0550
POISSON.DIST Probabilities Table |
||
X |
P(X) |
|
0 |
0.0550 |
|
1 |
0.1596 |
|
2 |
0.2314 |
|
3 |
0.2237 |
|
4 |
0.1622 |
|
5 |
0.0940 |
|
6 |
0.0455 |
|
7 |
0.0188 |
|
8 |
0.0068 |
x |
f |
f*x |
p |
200*p= expected value |
0 |
14 |
0 |
0.0550 |
11 |
1 |
31 |
31 |
0.1596 |
31.92 |
2 |
47 |
94 |
0.2314 |
46.28 |
3 |
41 |
123 |
0.2237 |
44.74 |
4 |
29 |
116 |
0.1622 |
32.44 |
5 |
21 |
105 |
0.0940 |
18.8 |
6 |
10 |
60 |
0.0455 |
9.1 |
7 |
5 |
35 |
0.0188 |
3.76 |
8 |
2 |
16 |
0.0068 |
1.36 |
Total |
200 |
580 |
199.4 |
Ho: number of arrivals follows Poisson distribution
H1: number of arrivals not follows Poisson distribution
Goodness of Fit Test |
||||
observed |
expected |
O - E |
(O - E)² / E |
|
14 |
11.000 |
3.000 |
0.818 |
|
31 |
31.920 |
-0.920 |
0.027 |
|
47 |
46.280 |
0.720 |
0.011 |
|
41 |
44.740 |
-3.740 |
0.313 |
|
29 |
32.440 |
-3.440 |
0.365 |
|
21 |
18.800 |
2.200 |
0.257 |
|
10 |
9.100 |
0.900 |
0.089 |
|
5 |
3.760 |
1.240 |
0.409 |
|
2 |
1.360 |
0.640 |
0.301 |
|
Total |
200 |
199.400 |
0.600 |
2.590 |
Chi square |
2.590 |
|||
DF |
8 |
Calculated chi square = 2.590 is < critical chi square at 0.05 level of significance value 15.51.
Ho is not rejected at 0.05 level.
Therefore Ho is not rejected at 0.01 level also.( critical value for 0.01 level is 20.09)
a. Poisson distribution was used to model the number of arrivals per minute at a bank...
The number of arrivals per minute at a bank located in the central business district a. Compute the mean number of arrivals per minute of a large city was recorded over a period of 200 minutes with the results shown in the table below. Complete parts a and b to the right (Type an integer or a decimal) Frequency 24 52 41 b. Compute the standard deviation for the number of arrivals per minute (Round to three decimal places as...
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes with the results shown in the table below. Complete parts a and b to the right. Arrivals Frequency 0 2222 1 3737 2 4242 3 3636 4 2828 5 2020 6 1010 7 44 8 11 a. Compute the mean number of arrivals per minute. μ= (Type an integer or a decimal. Do...
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes, with the results shown in the table below. Complete (a) through (c) to the right. a. Compute the expected number of arrivals per minute. b. Compute the standard deviation. c. What is the probability that there will be fewer than 2 arrivals in a given minute?
QUESTION 9 Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the expected value of X. 1.7 3 1.5 9
The number of automobiles entering a tunnel per 2-minute period follows a Poisson distribution. The mean number of automobiles entering a tunnel per 2-minute period is four. (A) Find the probability that the number of automobiles entering the tunnel during a 2minute period exceeds one. (B) Assume that the tunnel is observed during four 2-minute intervals, thus giving 4 independent observations, X1, X2, X3, X4, on a Poisson random variable. Find the probability that the number of automobiles entering the...
Customers arrive at a store randomly, following a Poisson distribution at an average rate of 20 per hour. What is the probability of exactly 3 arrivals in a 12 minute period?
The number of visitors to a webserver per minute follows a Poisson distribution. If the average number of visitors per minute is 4, what is the probability that: (i) There are two or fewer visitors in one minute? (2 points) (ii) There are exactly two visitors in 30 seconds? (2 points)
The mean number of homicides per year in one city is 151.0. Use a Poisson distribution to find the probability that in a given week there will be fewer than three homicides. (HINT: Assume a year is exactly 52 weeks.)
5)Visitors arrive to a water park according to a Poisson process with a mean of 3.30 visitors per minute. If the park opens at 8:00 am, what is the probability that no visitors arrive in a 3-minute period? Express your answer to four decimal places using conventional rounding methods. 7) Determine −z.05 Express your answer to two decimal places. 8) The probability that a standard normal random variable is equal to 0 is 0.50. T/F 10) The length of cracks...
1. According to the paper, what does lactate dehydrogenase (LDH) do and what does it allow to happen within the myofiber? (5 points) 2. According to the paper, what is the major disadvantage of relying on glycolysis during high-intensity exercise? (5 points) 3. Using Figure 1 in the paper, briefly describe the different sources of ATP production at 50% versus 90% AND explain whether you believe this depiction of ATP production applies to a Type IIX myofiber in a human....