Five fair die are rolled. What is the probability of at most two of the dice coming up a one or a six?
Your workings should show the use of appropriate laws and formulae — do not provide a purely arithmetic answer.
In: Statistics and Probability
A critical trial tests a method designed to increase the probability of conceiving a girl. In the study 300 babies were born, and 270 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born (?<p<?). Based on the result, does the method appear to be effective? yes or no.
In: Statistics and Probability
8. The probability that any child in a certain family will have blue eyes is ¼, and this feature is inherited independent by different children in the family. If there are five children in the family and it is known that at least one of these children has blue eyes, what is the probability that at least three of the children have blue eyes?
In: Statistics and Probability
6. A standard drug is used to treat a certain disease. The probability with which the drug is effective is 0.85. A new drug is developed and it is desired to determine if the new drug performs better than the standard. An experiment was conducted with which 300 people are given the new drug.
a. State symbolically the null and alternative hypotheses.
b. What is the critical value and rejection region of the proposed test?
c. If in fact, the success rate of the drug is 0.9, what is the power of the test?
d. When the experiment was actually carried out, it was found that the new drug was effective in 269 of the patients. Find the p-value of the test.
In: Statistics and Probability
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.
(a) What is the probability that among 8 randomly observed individuals exactly 4 do not cover their mouth when sneezing?
(b) What is the probability that among 18 randomly observed individuals fewer than 6 do not cover their mouth when sneezing?
(c) Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? Why?
In: Statistics and Probability
Consider the probability that no less than 21 out of 329 students will not pass their college placement exams. Choose the best description of the area under the normal curve that would be used to approximate binomial probability. OPTIONS ARE:
Area to the right of 20.5
Area to the right of 21.5
Area to left of 20.5
Area to left of 21.5
Area between 20.5 and 21.5
In: Statistics and Probability
Consider the probability that no less than 21 out of 329 students will not pass their college placement exams. Choose the best description of the area under the normal curve that would be used to approximate binomial probability. OPTIONS ARE:
Area to the right of 20.5
Area to the right of 21.5
Area to left of 20.5
Area to left of 21.5
Area between 20.5 and 21.5
In: Statistics and Probability
Assume that on a standardized test of 100 questions, a person has a probability of 80% of answering any particular question correctly. Find the probability of answering between 70 and 80 questions, inclusive. (Assume independence, and round your answer to four decimal places.)
P(70 ≤ X ≤ 80) =
In: Statistics and Probability
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is
0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.
(a) What is the probability that among 18 randomly observed individuals exactly 8 do not cover their mouth when sneezing?
(b) What is the probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?
(c) Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? Why?
In: Statistics and Probability
5 people walk into a room in random order. What is the probability that no person is in correct alphabetical position? For instance, if it is 4 people A, B, C, and D, and they walk in the order B, D, C, A then person C, having walked in 3rd, did have the correct alphabetical position?
In: Statistics and Probability