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…

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…

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…

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…

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…

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…

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…