Answer to Question #195104 in Statistics and Probability for fahmida

Question

Suppose that in Bangladesh, fifty percent people believe that the cricket team of Bangladesh  can defeat any cricket team around the world. For a sample of 20 people, make the following  calculations. 

a. Compute the probability that exactly 12 people believed that the cricket team of Bangladesh  can defeat any cricket team around the world. 

b. Compute the probability that no more than five people believed that the cricket team of  Bangladesh can defeat any cricket team around the world. 

c. How many people would you expect to say that the cricket team of Bangladesh can defeat any  cricket team around the world? 

d. Compute the variance and standard deviation of the number of people who believed that the  cricket team of Bangladesh can defeat any cricket team around the world.

Answer 1

(a).$P\left(12\:people\:believed\right)=\frac{1}{2\:}\times \frac{1}{20}\times \frac{1}{12}=\frac{1}{480}$

(b). $P\left(5\:people\:believed\right)=\frac{1}{2\:}\times \:\frac{1}{20}\times \:\frac{1}{5}=\frac{1}{200}$

(c). Number of people saying that the cricket team of Bangladesh can defeat any cricket team around the world is calculated as $\frac{1}{2}\times 20=10\:people.$

(d). Variance and standard deviation of number of people saying that the cricket team of Bangladesh can defeat any cricket team around the world is calculated as:

We need to compute the sample variance and standard deviation. These are the sample data that have been provided:

Now, we need to square all the sample values as shown in the table below:

The sample variance is computed as shown below:

$s^2=\frac{1}{n-1}\left(\sum _{i=1}^n\:\:X^2_1-\frac{1}{n}\left(\sum \:_{i=1}^nX_i\right)^2\right)$

$=\frac{1}{8-1}\left(284-\frac{44^2}{8}\right)$

$=6$

Based on the provided data, the sample variance is $S^2=6$ and the sample standard deviation $S^2=\sqrt{6}=2.4495$.