A test for extrasensory perception (ESP) involves asking a person to tell which of shapes—a circle, star, triangle, diamond, or heart—appears on a hidden computer screen. On each trial, the computer is equally likely to select any of the shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first shapes incorrectly but gets the fifth correct?
A correct answer is an option (c) .
A test for extrasensory perception (ESP) involves asking a person to tell which of shapes—a circle, star, triangle, diamond, or heart—appears on a hidden computer screen.
The number of positive outcomes divided by the total number of possible outcomes equals the probability:
Because the variable represents the number of tries required before a success, the distribution is geometric.
Geometric probability is defined as follows:
Evaluate at :
7. Benford’s law Refer to Exercise 5. The first digit of a randomly chosen expense account claim follows Benford’s law. Consider the events A = first digit is 7 or greater and B = first digit is odd.
(a) What outcomes make up the event A? What is P(A)?
(b) What outcomes make up the event B? What is P(B)?
(c) What outcomes make up the event “A or B”? What is P(A or B)? Why is this probability not equal to P(A) + P(B)?
86.in wins As a special promotion for its -ounce bottles of soda, a soft drink company printed a message on the inside of each cap. Some of the caps said, “Please try again,” while others said, “You’re a winner!” The company advertised the promotion with the slogan “in wins a prize.” Suppose the company is telling the truth and that every -ouncebottle of soda it fills has a-in-chance of being a winner. Seven friends each buy one -ounce bottle of the soda at a local convenience store. Let the number who win a prize.(a) Explain why is a binomial random variable.(b) Find the mean and standard deviation of . Interpret each value in context.
(c) The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the company’s -in- claim inaccurate? Compute and use the result to justify your answer.
Friends How many close friends do you have? An opinion poll asks this question of an SRS of adults. Suppose that the number of close friends adults claim to have varies from person to person with mean and standard deviation . We will see later that in repeated random samples of size 1100, the mean response x will vary according to the Normal distribution with mean and standard deviation . What is role="math" localid="1649504967961" , the probability that the sample result x estimates the population truth to within ?
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