Question

In a book the characters are trying to determine whether the Poisson probabilistic model can be used to describe the locations that rockets landed in a city. They divided the city into ​0.25-kmsquared regions. They then counted the number of rockets that landed in each​ region, with the results shown in the table below. Complete parts​ (a) through​ (e). Number of rocket hits 0 1 2 3 4 5 6 7 Observed number of regions 228 214 94 32 7 0 0 1 ​(a) Estimate the mean number of rocket hits in a region by computing mu equals Summation from nothing to nothing xP left parenthesis x right parenthesis.

Answer 1

Answer:

The estimated mean number of rockets hits in the region is 533.

Step-by-step explanation:

We are given the following information,

Number of rocket hits     |    Observed number of regions

0                                       |                       228

1                                        |                       214

2                                       |                        94

3                                       |                        32

4                                       |                         7

5                                       |                        0

6                                       |                        0

7                                       |                         1

We are asked to estimate the mean number of rocket hits in the region.

The mean or expected value is given by

$\mu = \sum (x \cdot P(x)) \\\\\mu = (0 \cdot 228) + (1 \cdot 214) + (2 \cdot 94) + (3 \cdot 32) + (4 \cdot 7) + (5 \cdot 0) + (6 \cdot 0) + (7 \cdot 1) \\\\\mu = 0 + 214 +188+ 96 +28 +0+ 0 + 7 \\\\\mu = 533$

Therefore, the mean number of rockets hits in the region is 533.