log(4) + log(2) - log(5)
= log(2²) + log(2) - log(5)
= 2 log(2) + log(2) - log(5)
= 3 log(2) - log(5)
= log(2³) - log(5)
= log (2³/5)
= log (8/5)
= log (1.6) = 0.2041... (rounded)
There's nothing preventing us from computing one integral at a time:



Expand the integrand completely:

Then

Since we are not given any information about the proportion, we will assume the sample proportion to be 0.50
so,
p = 0.50
The Error is 10% percentage point. This means that on either side of the population proportion the error is 5% so E = 0.05
z = 1.645 (Z value for 90% confidence interval)
The margin of error for population proportion is calculated as:
This means 271 students should be included in the sample
In order to do that we would need to see the list of potential answers.
Answer:
P ( X < 4 ) = 0.1736706
Step-by-step explanation:
Given:
- A random variable X follows a binomial distribution as follows,
Where n = 8, and p = 0.6.
Find:
- P ( X < 4 )?
Solution:
- The random variable X follows a binomial distribution as follows:
X ~ B ( 8 , 0.6 )
- The probability mass function for a binomial distribution is given as:
pmf = n^C_r ( p )^r (1-p)^(n-r)
- We are asked to find P ( X < 4 ) which is the sum of following probabilities:
P ( X < 4 ) = P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 )
- Use the pmf to compute the individual probabilities:
P ( X < 4 ) = 0.4^8 + 8^C_1*(0.6)*(0.4)^7 + 8^C_2*(0.6)^2*(0.4)^6 + 8^C_3*(0.6)^3*(0.4)^5 .
P ( X < 4 ) = 6.5536*10^-4 + 7.86432*10^-3 + 0.04128768 +0.12386304
Answer: P ( X < 4 ) = 0.1736706