Respuesta :
Answer: a= 0.0231
Step-by-step explanation:
n=8
p=0.75
q=1 - 0.75 = 0.25
(p=x)
p(5) = 8C5 (0.25)^5 (0.75)^8-5
p(5)= 0.0231
Or 2.31%
The probability that exactly 3 people from that group will go to Ches Tahoe restaurant is 2.11%
The probability that at least 35 people will go to Ches Tahoe the restaurant is -1.88.
Given that,
When you select a random person, the probability that this person will go to Ches Tahoe restaurant is 75%,
We have to determine,
You randomly select 8 people. What is the probability that exactly 3 people
from that group will go to Ches Tahoe restaurant.
You randomly select 50 people. Use the normal approximation to the binomial distribution to find the probability that at least 35 people will go to Ches Tahoe restaurant.
According to the question,
When you select a random person, the probability that this person will go to Ches Tahoe restaurant is 75%,
You randomly select 8 people.
Then,
The probability that exactly 3 people
from that group will go to Ches Tahoe restaurant is,
[tex]P(x) = ^nC_x \times q^x \times p^{n-x}[/tex]
Where n = 8, x = 5, q = 1 - 0.75 = 0.25, and p = 0.75
Substitute all the values in the expression,
[tex]P(5) = ^8C_5 \times (0.25)^5 \times (0.75)^{8-5}\\\\P(5) = \dfrac{8!}{(8-5)!. 5!} \times 0.00097 \times (0.75)^3\\\\P(5) = \dfrac{8 \times 7 \times 6}{3 \times 2} \times 0.00097 \times 0.42\\\\P(5) = 0.2118\\\\P(5) = 2.11 \ Percent[/tex]
The probability that exactly 3 people from that group will go to Ches Tahoe restaurant is 2.11%.
You randomly select 50 people. Use the normal approximation to the binomial distribution
Then, the probability that at least 35 people will go to Ches Tahoe restaurant is,
Mean for that at least 35 people will go to Ches Tahoe restaurant is,
[tex]\mu = n \times p \\\\\mu = 8 \times 0.75\\\\\mu = 6[/tex]
And standard deviation that at least 35 people will go to Ches Tahoe restaurant is,
[tex]\sigma = \sqrt{n \times p \times q} \\\\\sigma = \sqrt{0.75 \times 0.25 \times 8}\\\\\sigma = \sqrt{1.5}\\\\\sigma = 0.53[/tex]
Normal approximation to the binomial distribution is,
[tex]z = \dfrac{x-\mu}{\sigma}\\\\z = \dfrac{5-6}{0.53}\\\\z = \dfraac{-1}{0.53}\\\\z = -1.88[/tex]
The probability that at least 35 people will go to Ches Tahoe the restaurant is -1.88.
To know more about Probability click the link given below.
https://brainly.com/question/21586810
