An average of 2.5 visitors come to the barber’s during a day. Assume that the number of visitors is Poisson distributed. What is the probability that 4 visitors will come in one day? Find the standard deviation of the number of visitors per day
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An average of 2.5 visitors come to the barber’s during a day. Assume that the
number of visitors is Poisson distributed. What is the
in one day? Find the standard deviation of the number of visitors per day
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- The number of substances produced by a radioactive breakdown shows a Poisson distribution with a mean of 25. Use the Poisson distribution to find the probability that the number of substances occurring in 1 second is between 23 and 27.Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. a)What is the average number of cars in the garage (not including the parking lot)? b) How long (in minutes) do vehicles wait on average in the adjacent parking lot? c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the…A dean in the business school claims that GMAT scores of applicants to the school's MBA program have increased during the past 5 years. Five years ago, the mean and standard deviation of GMAT scores of MBA applicants were 550 and 60, respectively. 30 applications for this year's program were randomly selected and the GMAT scores recorded. If we assume that the distribution of GMAT scores of this year's applicants is the same as that of 5 years ago, find the probability of erroneously concluding that there is not enough evidence to supports the claim when, in fact, the true mean GMAT score is 590. Assume αα is 0.02.
- Malaysian families recorded an average of 17.2 kg of glass garbage each year with the standard deviation of the distribution is 2.5 kg. Using a central limit theorem, compute a probability that the mean of a sample of 55 families will be between 17 kg and 18 kg.Assume that your aunt wrote 139 letters to her family members in 2019. Let the random variable x represent the number of these letters that she wrote on a given day. Assume also that this scenario has a Poisson distribution. What is the mean number of letters written per day? Round to 3 decimal places. What is the standard deviation? Round to 3 decimal places.Suppose that the number of customers who enter a supermarket each hour is normally distributed with a mean of 650 and a standard deviation of 230. The supermarket is open 15 hours per day. What is the probability that the total number of customers who enter the supermarket in one day is greater than 10400? (Hint: Calculate the average hourly number of customers necessary to exceed 10400 in one 15-hour day.) Probability =
- Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -0.71°C.The average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. The number of shoppers is normally distributed. For a random day, what is the probability that there are between 200 and 400 shoppers at the grocery store? The answer should be typed as a decimal with 4 decimal places.Suppose collection of all quiz marks of a class of students is normally distributed with a mean of 7 and a standard deviation of 1. Calculate the probability that a student will receive a mark less than 5.
- Suppose that the duration of a particular type of criminal trial is known to have a mean of 18 days and a standard deviation of 6 days. We randomly sample 9 trials.Give the distribution of ΣX.Find the probability that the total length of the 9 trials is more than 188 days. 70 percent of the total of 9 of these types of trials will last more than how long? (Round your answer to two decimal places.)daysA technician can service an air conditioner in an average of one hour and fifteen minutes with a standard deviation of 20 minutes. (Assume the time is normally distributed). What is the probability that the technician can fix ten air conditioners in less than twelve hours?Americans receive an average of 20 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 5. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible.b. If an American is randomly chosen, find the probability that this American will receive no more than 23 Christmas cards this year. Incorrectc. If an American is randomly chosen, find the probability that this American will receive between 21 and 26 Christmas cards this year. d. 65% of all Americans receive at most how many Christmas cards? (Please enter a whole number)
