Cintas has installed three smoke detectors in its stockroom. The installer asserts that each detector is 90% likely to detect a fire within 30 seconds of ignition. Assuming the three detectors function independently, how likely is it that a fire will be detected within 30 seconds?

Cintas has installed three smoke detectors in its stockroom. The installer asserts that each detector is 90% likely to detect a fire within 30 seconds of ignition. Assuming the three detectors function independently, how likely is it that a fire will be detected within 30 seconds?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 340 trials, the touch therapists were correct 162 times. Complete parts (a) through (d). a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses? 0.5 (Type an integer or a decimal. Do not round.) b. Using Emily's sample results, what is the best point estimate of the therapists' success rate? 0.476 (Round to three decimal places as needed.) c. Using Emily's sample results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.…
To determine if chocolate milk was as effective as other carbohydrate replacement drinks, nine male cyclists performed an intense workout followed by a drink and a rest period. At the end of the rest period, each cyclist performed an endurance trial where he exercised until exhausted and time to exhaustion was measured. Each cyclist completed the entire regimen on two different days. On one day the drink provided was chocolate milk and on the other day the drink provided was a carbohydrate replacement drink. Data consistent with summary quantities appear in the table below. (Use a statistical computer package to calculate the P-value. Subtract the carbohydrate replacement times from the chocolate milk times. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.) Cyclist Time to Exhaustion (minutes) 1 2 3 4 5 6 7 8 9 ChocolateMilk 27.69 51.46 35.32 23.84 36.39 22.28 54.43 55.26 29.59…
As a student, you probably have noticed a curious phenomenon. In every class, there are some students who zip through exams and turn in their papers while everyone else is still on page 1. Other students cling to their exams and continue working until the very last minute. Have you ever wondered what grades these students get? Are the students who finish first the best in the class or are they simply conceding failure? To answer this question, we carefully observed a recent exam and recorded the amount of time each student spent working and the grade each student received. Is there a relationship between the two?a. Create a scatter plot of the datab.…
A sleep therapist wanted to see if a herbal tea advertised as a sleep aid really worked. He located 46 people with sleep problems and matched them into pairs on the basis of sleep problems and suggestibility. He then randomly assigned one person from each pair to drink the tea at bedtime (the experimental group), while the control group went to sleep as they normally did. He used an EEG to measure the minutes to sleep onset (the fewer the minutes to sleep onset, the better). He found MControl = 21.20, MExperimental = 19.70, sD = 5.47. Use an alpha of .05 and a two-tailed test to determine if the herbal teach was effective.
To determine if chocolate milk was as effective as other carbohydrate replacement drinks, nine male cyclists performed an intense workout followed by a drink and a rest period. At the end of the rest period, each cyclist performed an endurance trial where he exercised until exhausted and time to exhaustion was measured. Each cyclist completed the entire regimen on two different days. On one day the drink provided was chocolate milk and on the other day the drink provided was a carbohydrate replacement drink.Data consistent with summary quantities appear in the table below. (Use a statistical computer package to calculate the P-value. Subtract the carbohydrate replacement times from the chocolate milk times. Round your test statistic to two decimal places, your df down to the nearest whole number, and the P-value to three decimal places.) Cyclist Time to Exhaustion (minutes) 1 2 3 4 5 6 7 8 9 ChocolateMilk 48.65 55.02 53.71 38.49 40.59 54.20 28.85 26.64 58.97…
In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 340 trials, the touch therapists were correct 162 times. Complete parts (a) through (d). a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses? 0.5 (Type an integer or a decimal. Do not round.) b. Using Emily's sample results, what is the best point estimate of the therapists' success rate? (Round to three decimal places as needed.)
In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 331 trials, the touch therapists were correct 159 times. Complete parts (a) through (d). a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses? (Type an integer or decial. Do not round)
The human nervous system is extremely sensitive to changes in the environment. Stimuli that remain the same do not demand the same amount of attention as those that are new. You are a human factors psychologist working for a large automobile manufacturer. You have been assigned the task of determining what type of hot-engine warning system will be used on the next generation of small pickup trucks. The designers have given you three alternative systems: (a) a traditional temperature gauge that reads cold to the left, normal in the middle, and hot to the right; (b) a hot- engine warning light that flashes when the engine is about to overheat; and (c) a temperature gauge similar to (a), except that the entire gauge flashes on and off when the engine is about to overheat. You decide to test these three designs by having three separate groups of participants use the various warning systems in a driving simulator. The independent variable in this experiment is the type of warning system,…
A drug company creates a medicine designed to prevent colds, and states that it is equally effective for men and women. To test this claim, they give the medicine to 100 men and 200 women. At the end of the study, 33 men and 95 women caught a cold. Can we say that the drug is equally effective for men and women? (Use α = .01)
In North America, between 100 million and 1 billion birds die each year by crashing into windows on buildings, more than any other human-related cause. This figure represents up to 5% of all birds in the area. One possible solution is to construct windows angled downward slightly, so that they reflect the ground rather than an image of the sky to a flying bird. An experiment by Klem et al. (2004) compared the number of birds that died as a result of vertical windows, windows angled 20 degrees off vertical, and windows angled 40 degrees off vertical. The angles were randomly assigned with equal probability to six windows and changed daily; assume for this exercise that windows and window locations were identical in every respect except angle. Over the course of the experiment, 30 birds were killed by windows in the vertical orientation, 15 were killed by windows set at 20 degrees off vertical, and 8 were killed by windows set at 40 degrees off vertical. . Clearly state an appropriate…
The owner of a small firm has just purchased a personal computer, which she expects will serve her for the next two years The owner has been told that she "must" buy a surge suppressor to provide protection for her new hardware against possible surges or variations in the electrical current, which have the capacity to damage the computer The amount of damage to the computer depends on the strength of the surge. It has been estimated that there is a 1% chance of incurring 350 dollar damage, 4% chance of incurring 200 dollar damage, and 10% chance of incurring 125 dollar damage from a surge within the next two years. An inexpensive suppressor, which would provide protection for only one surge, can be purchased. How much should the owner be willing to pay if she makes decisions on the basis of expected value? Expected value = Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining.
A 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it. A 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it. Among 257 trials, the touch therapists were correct 105 times. Use a 0.01 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective?