A breath analyzer is used by the police to estimate blood alcohol content (BAC) from a breath sample. If a person’s BAC is above (or equal to) the legal limit, they can be arrested for suspicion of driving while impaired from alcohol. However, the only way to accurately measure BAC level is through taking a blood sample; a number of factors are known to influence the results of breath analyzers, such as hypoglycemia.
A particular brand of breath analyzer is accurate about 80% of the time. That is, if an individual actually has BAC equal to or above the legal limit, the device indicates a positive result with probability 0.80, and if an individual actually has BAC below the legal limit, the device indicates a negative result with probability 0.80.
a.) Suppose that on any particular Saturday night, about 5% of drivers are known to be driving under the influence.
i. Calculate the probability that a driver who tests positive actually has BAC level equal to or above the legal limit.
ii. How accurate would the device need to be for the probability in part i. to be 0.80?
iii. In language accessible to someone who has not taken a statistics course, explain why the probability in part i. is much lower than the accuracy of the breath analyzer. Limit your answer to at most five sentences.
In: Statistics and Probability
A salesman normally makes a sale (closes) on 75% of his presentations. Assuming the presentations are independent, find the probability of each of the following.
a) He fails to close for the first time on his fifth attempt.
b) He closes his first presentation on his fourth attempt.
c) The first presentation he closes will be on his second attempt.
d) The first presentation he closes will be on one of his first three attempts.
A manufacturer of game controllers is concerned that its controller may be difficult for left-handed users. They set out to find lefties to test. About 13% of the population is left-handed. If they select a sample of 6 customers at random in their stores, what is the probability of each of the outcomes described in parts a through f below?
a) The first lefty is the fourth person chosen.
The probability is _____________
(Round to four decimal places as needed.)
The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. Complete parts a and b below.
Repair Calls 1 2 3 4
Probability .1 .4 .3 .2
b) What is the standard deviation?
The standard deviation is ____________
(Round to two decimal places as needed.)
In: Statistics and Probability
A girl scout and her mom are setting up a table to sell cookies
in front of a
grocery store. They have available 6 boxes of Samoas, 6 boxes of
Tagalons, 2 boxes of
Do-si-dos, and 6 boxes of Trefoils. Each box sells for $5.
Suppose that, immediately after they finish setting up, the
first customer shows up, and he
purchases 4 boxes of cookies. Determine the probability
distribution function for the number of
Tagalons purchased.
Draw the cumulative distribution function for the number of Tagalons purchased.
In: Statistics and Probability
The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below. . Find the probability of getting exactly 1 girl in 8 births. P(x) Number of Girls x P(x) 0 0.002 1 0.022 2 0.117 3 0.227 4 0.264 5 0.227 6 0.117 7 0.022 8 0.002
In: Statistics and Probability
In: Statistics and Probability
A standard deck of playing cards consists of the four suits (diamond, club, heart, spade) and each suit contains 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King). Suppose ve cards are taken from an ordinary deck of 52 cards. Calculate the following: a) total number of 5-card-combinations b) number of 5-card-combinations where all 5 cards are hearts c) probability that all 5 cards are of the same suite
In: Statistics and Probability
Suppose the daily number of parking tickets issued on campus has a mean of 1.4 tickets and a standard deviation 1.2 tickets.
a) If we consider a semester as a random sample of 80 days, give the properties (and provide a sketch) for the sampling distribution for the sample mean number of tickets per day.
b) Find the probability the semester will have a sample mean of more than 1.5 tickets per day.
c) Could the population of tickets issued on individual days have a normal distribution? Explain why or why not.
In: Statistics and Probability
25% of Flapper fish have red spots, the rest have blue spots. A fisherman nets 10 flapper fish. What are the probabilities that:
(i) exactly 8 have blue spots ?
(ii) atleast 8 have blue spots ?
A large number of samples, each of 100 flapper fish are taken.
(iii) What is the mean and standard deviation of the number of red spotted fish per sample ?
(iv) What is the probability of a sample of 100 flapper fish containing over 30 with red spots ?
In: Statistics and Probability
Use the following information for this and the next question. In 2019, the mean duration of unemployment for a person is 21.6 weeks. Assume that the population standard deviation is 5 weeks. You would like to conduct a follow-up study, so you select a sample of 40 unemployed people. You need to look into the sampling distribution of the mean number of weeks of unemployment.
What is the mean and standard deviation of that distribution? What is the probability that in a sample of 40 unemployed people, the mean number of weeks of unemployment is within 1 week of the population mean?
In: Statistics and Probability
The number of hits to a website follows a Poisson process. Hits occur at the rate of 0.8 per minute between 7:00 P.M. and 9:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 8:39 P.M. and 8:47 P.M. Interpret each result.
(a) exactly seven P(7)=
(Round to four decimal places as needed.)
(b) fewer than seven
(c) at least seven
(Round to four decimal places as needed.)
In: Math