The units without evidence of gas leaks or electrical failure showed other types of failure. If this is a representative sample of AC failure, find the probability a. That failure involves a gas leak b. That there is evidence of electrical failure given that there was a gas leak c. That there is evidence of a gas leak given that there is evidence of electrical failure
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- A student selects a random sample of 145 students from her large high school. For each student, she records the grade level and their favorite type of pet. She would like to know if there is convincing evidence that grade level is associated with type of pet. Let a = 0.05. The observed and expected counts are displayed in the tables. Observed counts: Pet Dog Cat Bird Other Ninth and Tenth 21 15 8 30 Grades Eleventh and Grade 24 12 11 24 Twelfth Grades Expected counts: Pet Dog Cat Bird Other Ninth and Tenth 23.0 13.8 9.7 27.6 Grades GradeA space agency compiles data on space-shuttle launches and publishes them on its website. The following table displays a frequency distribution for the number of crew members on each shuttle mission over a 30-year period. Let X denote the crew size on a randomly selected shuttle from this time period. Complete parts (a) through (e) below. Crew size 2 4 5 6 7 8 Frequency 4 5 40 20 72 1 a. What are the possible values of the random variable X? (Use a comma to separate answers as needed.) b. Use random-variable notation to represent the event that the shuttle mission obtained has a crew size of 7. Select the correct choice below and fill in the answer box within your choice. A.( P) B. c. Find P(X=4); interpret in terms of percentages. P(X=4)= (Round to three decimal places as needed.) Interpret in terms of percentages. Select the correct choice below and fill in the answer box to complete…Two different professors teach an introductory statistics course. The table shows the distribution of final grades they reported. We wonder whether one of these professors is an "easier" grader. Answer parts a) and b) below. Prof. Alpha Prof. Betal A 6. 11 B. 6. 14 12 Below C 11 4. 11 C.... a) Find the expected counts for each cell in this table. Prof. Alpha Prof. Beta (Round to two decimal places as needed.) A B Below C b) Test the hypothesis about the two professors, and state an appropriate conclusion. (Assume a significance level of a= 0.05) State the appropriate null and alternative hypotheses. Choose the correct answer below. O A. Ho: The grade distributions are different. HA: The grade distribution is the same for both professors. O B. Ho: The grade distribution is the same for both professors. Ha: Professor Beta gives out more C's than Professo Alpha. OC. H: The grade distribution is the same for both professors. HA: Professor Alpha gives out more A's than Professor Beta. OD.…
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- A certain virus affects 0.7% of the population. A test used to detect the virus in a person is positive 88% of the time if the person has the virus (true positive) and 13% of the time if the person does not have the virus (false positive) Fill out the remainder of the following table and use it to answer the two questions below based on a total sample of 100,000 people. a. Find the probability that a person has the virus given that they have tested positive. Round your answer to the nearest hundredth of a percent and do not include a percent sign. b. Find the probability that a person does not have the virus given that they test negative. Round your answer to the nearest hundredth of a percent and do not include a percent sign.The probability is 0.4 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In six traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a. exactly three; at least three; at most three. b. between two and four, inclusive. c. Find and interpret the mean of the random variable Y. a. The probability that exactly three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) The probability that at least three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) The probability that at most three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) b. The probability that between two and four…According to a recent study, 3 in every 8 women has been a victim of domestic abuse. This probability was obtained from a survey of 1,000 adult women. Suppose we randomly sample 25 women and find that 7 have been abused. Complete parts a through c below. G a. What is the probability of observing 7 or more abused women in a sample of 25 if the proportion p of women who are victims of domestic abuse is really p= ㅎ? The probability of observing 7 or more abused women in a sample of 25 is (Round to four decimal places as needed.)
- Suppose that a plaque in an elevator contains the following statement: Maximum weight 3500 pounds or 18 people. What is the probability that this elevator will be overloaded given that the weight of men is normally distributed with a mean of 179.2 pounds and a standard deviation of 29.6 pounds? A. 0.3468 O B. 0.0144 O C. 0,6532 O D. 0.9856Suppose that skiing injuries occur at a constant rate, are statistically independent of each other, and the amount of time required to treat each injury follows an approximately normal distribution with a mean of 80 minutes and a standard deviation of 20 minutes. Assume the average ski injury rate is 2.6 injuries per 1,000 skier-days, and the treatment time is independent of the number of injuries treated on any day. a. In a week with 150 skiers each day, what is the probability there is at least 1 injury on each day? b. In a week with 150 skiers each day, what is the probability there is at least 1 injury on at least 5 of the 7 days? c. On a day with 7 injuries, what is the probability that at least 5 of the 7 injuries require more than 100 minutes to treat the injury? d. In a week with 7 injuries, what is the probability that at least 5 of the 7 injuries require more than 100 minutes to treat the injury?Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases, so it is important that the information on packages be accurate. Suppose that a random sample of n = 12 frozen dinners of a certain type was selected and the calorie content of each one was determined. Below are the resulting observations, along with a boxplot and normal probability plot.