For the past 104 years, a certain state suffered 27 direct hits from major (category 3 to 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts (a) through (d). a) What is the probability that the state will not be hit by any major hurricanes in a single year? The probability is nothing. (Round to four decimal places as needed.) (b) What is the probability that the state will be hit by at least one major hurricane in a single year? The probability is nothing. (Round to four decimal places as needed.) Is this unusual? Yes No (c) What is the probability that the state will be hit by at least three major hurricanes in a single year, as happened last year? The probability is nothing. (Round to four decimal places as needed.) Does this indicate that the 2004 hurricane season in this state was unusual?
In: Math
Based on a poll, among adults who regret getting tattoos, 18% say that they were too young when they got their tattoos. Assume that six adults who regret getting tattoos are randomly selected, and find the indicated probability. Complete parts (a) through (d) below. a. Find the probability that none of the selected adults say that they were too young to get tattoos. nothing (Round to four decimal places as needed.) b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos. nothing (Round to four decimal places as needed.) c. Find the probability that the number of selected adults saying they were too young is 0 or 1. nothing (Round to four decimal places as needed.) d. If we randomly select six adults, is 1 a significantly low number who say that they were too young to get tattoos? ▼ Yes, No, because the probability that ▼ more than 1 at least 1 exactly 1 less than 1 at most 1 of the selected adults say that they were too young is ▼ greater than equal to less than 0.05.
In: Statistics and Probability
-A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc.). While none had more than three of thesedefects,
6% had three, 12% had two, and 26% had one defect. Find the expected number of appearance defects in a new car and the standard deviation. Compute the expected value of the number of appearance defects.
E(appearance
defects)equals=. 68.68
(Round to two decimal places as needed.)
Compute the standard deviation of the number of appearance defects.
SD(appearance
defects)equals= _____________________
(Round to two decimal places as needed.)
-A salesman normally makes a sale (closes) on 70% 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 sixth attempt.
b) He closes his first presentation on his fifth 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 11% of the population is left-handed. If they select a sample of 99 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 third person chosen.The probability is _____________________
(Round to four decimal places as needed.)
b) There are some lefties among the 99 people.The probability is _______________________
(Round to four decimal places as needed.)
c) The first lefty is the second or third person. The probability is __________________________
(Round to four decimal places as needed.)
d) There are exactly 3 lefties in the group. The probability is __________________________
(Round to four decimal places as needed.)
e) There are at least 3 lefties in the group. The probability is __________________________
(Round to four decimal places as needed.)
f) There are no more than 3 lefties in the group. The probability is _________________________
(Round to four decimal places as needed.)
In: Statistics and Probability
A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 11.2 m/s and accelerates at the rate of 0.3 m/s2 for 6.9 s.
a)The racer continues at this velocity to the finish line. If he was 293 m from the finish line when he started to accelerate, how much time did he save (in s)?
b)One other racer was 5 m ahead when the winner started to accelerate, but he was unable to accelerate, and traveled at 11.5 m/s until the finish line. How far ahead of him (in seconds) did the winner finish?
c) How far ahead of him (in meters) did the winner finish?
A fast elevator in a skyscraper is employing the following scheme to get from the starting level to the desired level: For the first half of the time it accelerates at the maximum allowed acceleration of 1.0 m/s2 and for the second half it decelerates at the maximum allowed acceleration of −1.0 m/s2. How long does it take (in seconds) to go from ground level to the highest level at 80 m elevation?
A track team is practicing for a 4 × 100 m relay race. The first runner, Linda, is running at a constant speed of 8.6 m/s. The next runner, Jenny, will be starting from rest at the 80 m mark. She has an acceleration of 1.0 m/s2. Ideally the two runners meet at the 100 m mark to hand over the baton. At this point, Jenny is still accelerating.
a) How long does it take Jenny to run from the 80-m mark to the 100-m mark?
b) At what distance behind Jenny should Linda be when Jenny starts running? (Assume for simplicity that there is no distance between the two runners when the switch happens.)
c) What’s Jenny’s speed at the 100m mark?
In: Physics
ROULETTE is a casino game where a numbered wheel spins and a steel ball falls into a location marked by one particular colored number. In the United States there are 18 locations colored red, 18 locations colored black and 2 locations colored green. The red and black locations are numbered 1-36 and the green locations are labeled "0" and "00" as shown in the picture to the right. The wheel therefore has 38 locations in total. Note that the odd and even values are not evenly distributed within each color. For any particular wager a player makes, an expected profit can be calculated from: Expected profit = (Prob. of winning) x (winning payout amount) - wager
(c) Another potential wager is to "bet on odd" which has the same payout as betting on black, but wins only when the ball lands in a location with an odd number of either color. If the ball lands on an even numbered location or a green space you lose your wager and the payout would be $0. What is the expected profit from placing two bets on a single spin - $17 on black and $19 on odd? (round to closest penny)
In: Statistics and Probability
Suppose that 52% of the people have been vaccinated. If 25 people are randomly selected, answer the following questions.
(a) [1] What is the probability that exactly 12 of them have been vaccinated?
(b) [2] What is the probability that at least 10 of them have been vaccinated?
(c) [2] Determine the probability that between 11 and 15 (including 11 and 15) of them have been vaccinated.
(d) [2] What is the expected number of of them have been vaccinated and its standard deviation?
In: Statistics and Probability
An experiment consists of rolling three fair dice --- a red die, a blue die, and a white die --- and recording the number rolled on each die. Assume that the dice are fair, so that all outcomes are equally likely. (1) What probability should be assigned to each outcome? equation editorEquation Editor (2) What is the probability that the sum of the numbers rolled is 5? equation editorEquation Editor (3) What is the probability that the sum of the numbers rolled is at most 6? equation editorEquation Editor
In: Statistics and Probability
In: Statistics and Probability
In: Statistics and Probability
A bank has kept records of the checking balances of its 4000 customers and determined that the average daily balance of its customers is $300 with a standard deviation of $48. A random sample of 144 checking accounts is selected. Please answer the following questions.
(a) What is the probability that the sample mean will be more than $309?
(b) What is the probability that the sample mean will be between $291 and $307?
(c) Suppose the number of customers decreases from 4000 to 2000. What is the probability that the sample mean will be between $296 and $306?
In: Statistics and Probability