Respuesta :
Answer:
n = 50
Step-by-step explanation:
The rules for determining if a sample proportion is normally distributed are:
1. np >= 10
2. n(1-p)>=10
If both of these conditions are met then the sample is normally distributed.
We are given p = 4/5 or 0.80.
So, n(0.80)>=10
Step 1. We must determine what the lowest value n can be to make this statement true.
Using the guess and check method we find 13(0.80)>=10
Step 2. We must determine what the lowest value n can be to make this statement true. n(1 - 0.80)>=10.
Using the guess and check method we find 50(1-0.80)>=10
Thus the lowest value n can be that meets both requirements is 50.
Answer:
The smallest value of [tex]n[/tex] for which the distribution will be normal is 50.
Step-by-step explanation:
Given information:
The value of probability [tex]p=4/5[/tex]
As, for the smallest value of n that satisfies the requirement for normally distributed probability one need to satisfy the two statements:
(1) [tex]n(p)\geq 10[/tex]
(2) [tex]n(1-p)\geq 10[/tex]
If, both of these condition is satisfied then the sample will be normally distributed:
As, [tex]p=0.80[/tex]
So,
[tex]n(0.80)\geq 10\\n\geq 12.5[/tex]
Now, we need to guess a number grater then 12.5 which satisfy the second statement:
As we choose 50 as our guess
So,
[tex]n(1-p)\geq 10\\50(1-0.80)\geq 10[/tex]
Hence, the above condition is valid for n=50
Hence, the smallest value of n for which the distribution will be normal is 50.
For more information visit:
https://brainly.com/question/12905909?referrer=searchResults
