At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
The required probabilities are calculated by using the binomial distribution formula as below:
a. The probability that 5 will still be with the company after 1 year is P(x = 5) = 0.2541
b. The probability that 5 or more still be with the company after 1 year is 0.8057.
What is the binomial distribution formula?
The binomial distribution formula for finding the required probability of a random variable is
[tex]P(X = r) = _nC_rp^rq^{n-r}[/tex]
Where
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
p = probability of success
q = 1 - p = probability of failure
n = total number of trials
r = number of trials chosen
Calculation:
It is given that,
n = 8 and p = 0.7
Then, q = 1 - 0.7 = 0.3
a. The probability that 5 will still be with the company after 1 year:
P(X = 5) = [tex]_8C_5[/tex] (0.7)⁵(0.3)⁸⁻⁵
⇒ [tex]\frac{8!}{5!(8-5)!}[/tex] (0.7)⁵(0.3)³
⇒ 0.2541
Therefore, the probability P(x = 5) is 0.254.
b. The probability that 5 or more still be with the company after 1 year:
More than 5 means 6, 7, and 8
So,
P(X = 6) = [tex]_8C_6[/tex] (0.7)⁶(0.3)⁸⁻⁶
⇒ [tex]\frac{8!}{6!(8-6)!}[/tex] (0.7)⁶(0.3)²
⇒ 0.2964
P(X = 7) = [tex]_8C_7[/tex] (0.7)⁷(0.3)⁸⁻⁷
⇒ [tex]\frac{8!}{7!(8-7)!}[/tex] (0.7)⁷(0.3)¹
⇒ 0.1976
P(X = 8) = [tex]_8C_8[/tex] (0.7)⁸(0.3)⁸⁻⁸
⇒ [tex]\frac{8!}{8!(8-8)!}[/tex] (0.7)⁸(0.3)⁰
⇒ 0.0576
Thus, the probability that 5 or more still be with the company after 1 year
= P(5) + P(6) + P(7) + P(8)
= 0.2541 + 0.2964 + 0.1976 + 0.0576
= 0.8057.
Therefore, the required probabilities are 0.2541 and 0.8057.
Disclaimer: The question given in the portal is incomplete. Here is the complete question.
Question: If the probability of a new employee in a fast-food chain still being with the company at the end of the year is 0. 7, what is the probability that out of 8 new hired people:
a. 5 will still be with the company after 1 year?
b. 5 or more still be with the company after 1 year?
Learn more about binomial distribution here:
https://brainly.com/question/15246027
#SPJ1
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
