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- 2) In a three-digit lottery, each of the three digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table to the right summarizes the frequency of occurrence of each digit for 90 consecutive daily three-digit drawings. The table also appears in the Lottery worksheet of the Chp 12 HW Problems data workbook on Moodle. a) What is the appropriate null and alternate hypothesis to determine if the digits are not random? b) Choose a level of a Use a = 0.05 for this problem. c) Sketch the sampling distribution. Include the critical value and test statistic d) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem. e) What is the p-value for the hypothesis test.From long experience a landlord knows that the probability an apartment in a complex will not be rented is 0.10. There are 20 apartments in the complex, and the rental status of each apartment is independent of the statue of the others. When a minimum of 16 apartments are rented, the landlord can meet all monthly expenses. a) What is the probability that exactly 4 units are unrented? Round to 4 decimal places. b) What is the probability that four or fewer units are unrented? Round to 4 decimal places. c) In any given month, what is the probability that the landlord will not meet the monthly expenses? Round to four decimal places. d) Which probability is more relevant to the landlord in terms of being able to meet monthly expenses7. A company that packages peanuts states that a maximum of 6% of the peanut shells contains no nuts. At random, 300 peanuts were selected and 21 of them were empty. At 0.05 CI, determine if the claims is true.
- 6a) During the Restricted Movement Order (RMO), the maximum number of people can ride on a 7-seater car is only 4 people. In how many ways can a family of 10 people be seated on the car if the father must be on the car? In how many ways can the word ASTRAZENECA be arranged if the arrang ent must start with Z? b) The probability that a particular day will be sunny is 0.6. The probability that Aisyah will be going for a shopping on a sunny day is 0.6 and the probability that she will begoing for a shopping on a rainy day is 0.2. a) Draw a tree diagram to represent the above information. If Aisyah goes for a shopping on a particular day, find the probability that it is a rainy day. b)a) The alternative way to travel from Seremban to Kuala Lumpur is by the KTM Seremban toKuala Lumpur Sentral Commuter Train that operates many trips a day starting from theearly morning until the late evening. Every trip takes 1 hour and 25 minutes. It is assumedthat the train arrives at Kuala Lumpur Sentral uniformly between 0 and 110 minutes. i) Calculate the probability that the train takes between 40 and 90 minutes to arrive atKuala Lumpur Sentral. ii) What is the average time taken to travel from KTM Seremban to Kuala LumpurSentral?
- a) Ellisa is going to play one badminton match and one tennis match. The badminton match has been scheduled one week earlier than the tennis match. Based on the prediction by her coach, the chance that she will win the badminton match is 0.9. Other than that, the coach believed that if Ellisa wins the badminton match, the chance that she will win the tennis match is 0.65. But if she loses the badminton match, she has a 0.7 chance of losing the tennis match too. i) Draw a tree diagram and the probabilities for each event involved in the above scenario. ii) Find the probability that Ellisa will win the tennis match. iii) Are the events independent? Proof it numerically. b) According to a survey conducted by Tourism Malaysia, 70% of Malaysian companies give employees 25 to 30 days of annual leave. Find the probability that among 6 companies surveyed at random, more than half of the companies give employees 25 to 30 days of annual leave. c) The time taken for servicing a car has an average…1. Which of the following is an example of time series problem? a. Estimating number of covid 19 patients in next 6 months. b. Estimating the total sales in next 3 years of an insurance company. c. Estimating your CGPA for Summer 2021. a) Only a b) Only b c) Only a & b d) All 3 of them 2. Which of the following can't be a component for a time series plot? a) Seasonality b) Trend c) Cyclical d) None of the above 3. If the demand is 100 during October 2016, 200 in November 2016, 300 in December 2016, 400 in January 2017. What is the 3-month simple moving average for February 2017? a) 300 b) 350 c) 400 d) Need more information 4. A regression equation for weight (y variable) and height (x variable) for 55 college students gave an error sum of squares (SSE) of 10.7 and a total sum of squares (SSTO) of 85.2. The proportion of variation explained by x, R³, is a) 11.2% b) 87.4% c) 88.6% d) None of the aboveSuppose that a point is randomly chosen from a segment with a length of 12 units. What is the probability that no of two smaller segments is more than twice as long as the other? ROUND OFF your answer in DECIMAL FORM (4 decimal places)
- State Jenson's inequality on expectation.a) Determine the probability that a randomly selected call was during the week. The probability is----- (Round to three decimal places as needed.) b. Determine the probability that a randomly selected call was less than 20 minutes. The probability is----- (Round to three decimal places as needed.) c. Determine the probability that a randomly selected call was 10 to less than 20 minutes. The probability is----- (Round to three decimal places as needed.) A call center for customer support records the time each customer requires for service and whether the call occurred during the week (Monday through Friday) or during the weekend (Saturday and Sunday). The results are shown in the accompanying table. Complete parts a through h. Time (minutes) Week Weekend Less than 5 15 4 5 to less than 10 27 3 10 to less than 15 12 8 15 to less than 20 23 5 More than 20 10 14The access code for a safe consists of three digits. Each digit can be any number from 1 through 7, and each digit can be repeated. Complete parts (a) through (c). (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is nothing. (b) What is the probability of randomly selecting the correct access code on the first try? The probability of randomly selecting the correct access code is nothing. (Round to three decimal places as needed.) (c) What is the probability of not selecting the correct access code on the first try? The probability of not selecting the correct access code is nothing. (Round to three decimal places as needed.)
