Binomial Distribution Archives - Page 4 of 5

Binomial Probability Distribution

Take a guess: A student takes a multiple-choice test that has 9 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Round the answers to at least four decimal places. Find the probability that X is equal to 4:

Answer:Given: Probability of success $(p) = \frac{1}{4} = 0.25$ Sample size $(n) = 9$ Solution:The probability that x is equal to 4: $P (x = 4) = (\binom{9}{4}) \cdot {0.25}^{4} \cdot (1 - 0.25)^{9 - 4} = 0.1168$ Final Answer:The probability that…

Binomial Probability Distribution

Take a guess: A student takes a multiple-choice test that has 12 questions. Each question has six choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Round the answers to at least four decimal places. Find the probability that X is equal to 6:

Answer:Given: Probability of success $(p) = \frac{1}{6} = 0.1667$ Sample size $(n) = 12$ Solution:The probability that x is equal to 6: $P (x = 6) = (\binom{12}{6}) \cdot {0.1667}^{6} \cdot (1 - 0.1667)^{12 - 6} = 0.0066$ Final Answer:The probability that…

Binomial Probability Distribution

Take a guess: A student takes a multiple-choice test that has 8 questions. Each question has five choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Round the answers to at least four decimal places. Find the probability that X is equal to 5:

Answer:Given: Probability of success $(p) = \frac{1}{5} = 0.20$ Sample size $(n) = 8$ Solution:The probability that x is equal to 5: $P (x = 5) = (\binom{8}{5}) \cdot {0.2}^{5} \cdot (1 - 0.2)^{8 - 5} = 0.0092$ Final Answer:The probability that…

Binomial Probability Distribution

Take a guess: A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Round the answers to at least four decimal places. Find the probability that X is equal to 3:

Answer:Given: Probability of success $(p) = \frac{1}{4} = 0.25$ Sample size $(n) = 10$ Solution:The probability that x is equal to 3: $P (x = 3) = (\binom{10}{3}) \cdot {0.25}^{3} \cdot (1 - 0.25)^{10 - 3} = 0.2503$ Final Answer:The probability…

Binomial Probability Distribution

Take a guess: A student takes a multiple-choice test that has 7 questions. Each question has five choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Round the answers to at least four decimal places. Find the probability that x is equal to 4:

Answer:Given: Probability of success $(p) = 1 / 5 = 0.20$ Sample size $(n) = 7$ Solution:The probability that x is equal to 4: $P (x = 4) = (\binom{7}{4}) \cdot {0.2}^{4} \cdot (1 - 0.2)^{7 - 4} = 0.0287$ Final Answer:The probability that…

Binomial Probability Distribution

For a binomial random variable x with n=8 and p=0.2, find P(x≤1) using the cumulative table.A. 0.503B. 0.168C. 0.797D. 0.056

Answer:Given: Probability of success $(p) = 0.2$ Sample size $(n) = 8$ Solution:The probability that x is less than or equal to 1: $P (x \leq 1) = \sum_{0}^{1} (\binom{n}{x}) \cdot p^{x} \cdot (1 - p)^{n - x} = \sum_{0}^{1} (\binom{8}{x}) \cdot {0.2}^{x} \cdot (1 - 0.2)^{8 - x} = 0.5033$ Final…

Binomial Probability Distribution Blog

31% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. If convenient, use technology to find the probabilities.

Answer: Given: Probability of success $(p) = 0.31$ Sample size $(n) = 10$ Solution: → The probability that the number of college students who say they use credit cards because of the rewards program is: (A) Exactly 2: $P(x = 2) = \binom{n}{x} p^x…

Binomial Probability Distribution

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n=10,p=0.8,x=8

Answer: Given: Probability of success $(p) = 0.8$ Sample size $(n) = 10$ Solution: The probability that x is equal to 8: $P (x = 8) = (\binom{n}{x}) p^{x} (1 - p)^{n - x} = (\binom{10}{8}) {0.8}^{8} (1 - 0.8)^{10 - 8} = 0.3020$

Binomial Probability Distribution

The Alvin Secretarial Service procures temporary office personnel for major corporations. They have found that 40% of their invoices are paid within ten working days. A random sample of 12 invoices is checked. What is the probability that exactly 10 of the invoices will be paid within ten working days?

Answer: Given : The probability of success, $p = 0.40$ The sample size, $n = 12$ Solution : → The probability that exactly 10 of the invoices will be paid within ten working days : $$P(x = 10) = \binom{n}{x} p^x (1 – p)^{n…

Binomial Probability Distribution

According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267.

(a) Using the binomial distribution, what is the probability that among 10 randomly observed individuals, exactly 8 do not cover their mouth when sneezing? Answer: Given: The probability of success, $p = 0.267$ The sample size, $n = 10$ Solution: → The probability that…