1. A study undertaken by the University Hospital of the West Indies (UWHI) found that the number of patients admitted with the COVID-19 virus each day can be modeled by a Poisson distribution with a mean of 2.5 patients being admitted each day. a. i) Calculate P(X=2) b. ii) Hence, determine the probability that exactly 2 patients will be admitted in three consecutive days. Find the probability that at least 12 patients will be admitted in a one-week period. c. State two assumptions implied by using a Poisson distribution to model the number of patients contracting COVID-19.
Added by Jermaine R.
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5, we can use the Poisson probability formula to calculate the probability of exactly 2 patients being admitted in one day. P(X=k) = (e^(-λ) * λ^k) / k! where λ = 2.5 and k = 2 P(X=2) = (e^(-2.5) * 2.5^2) / 2! P(X=2) = (0.0821 * 6.25) / 2 P(X=2) = Show more…
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Lien L.
6. Suppose that the mean number of customers who arrive per minute at the bank during the noon-to-1 P.M. hour is equal to 3. (Hint: Poisson Distribution) a) What is the probability that in a given minute, exactly two customers will arrive? b) What is the probability that more than two customers will arrive in any given minute? 7. The number of work-related injuries per month in a manufacturing plant is known to follow a Poisson distribution with a mean of 2.5 work-related injuries a month. (Hint: Poisson Distribution) a) What is the probability that in any month, no work-related injuries occur? b) What is the probability that at least one work-related injury occurs? 8. From an inventory of 30 cars being shipped to a local automobile dealer, 4 are SUVs. What is the probability that if 4 cars arrive at a particular dealership? a) all 4 are SUVs? b) none are SUVs? c) at least 1 is an SUV? 9. A carton of orange juice has a volume which is normally distributed with a mean of 120ml and a standard deviation of 1.8ml. Find the probability that the volume is more than 118ml. 10.The pulse rate is a measure of the number of heart beats per minute. Suppose that the pulse rates for adults are assumed to be normally distributed with a mean of 78 and a standard deviation of 12. Find the probability that adults will have the pulse rates between 60 and 100. 11.In January 2003, the American worker spent an average of 77 hours logged on to the internet while at work. Assume that the population mean is 77 hours, the times are normally distributed, and the standard deviation is 20 hours. A person is classified as heavy user if he or she is in the upper 20% of usage. How many hours did a worker have to be logged on to be considered a heavy user?
Karan D.
A useful binomial calculator and Poisson calculator. You may round your responses to 3 decimal places. When naming a distribution, include the relevant specifications (Binomial - n, p ; Poisson - ÎĽ). To create a PDF for a Poisson distribution (which could have an infinite number of entries), you may group all values including and above the first value of the random variable with a probability below 1%. Problem 1 A medical researcher at a Seattle hospital is conducting a study on asthma in Washington. According to the CDC about 9.6% of the population in Washington has asthma. If the researcher selects 3 participants at random each day, she is interested in how likely it is that some of them will have asthma. Let A = the number of participants with asthma out of 3 participants. Determine the distribution A follows. If it follows a known distribution, construct the PDF for A. Problem 2 At the same hospital, an average of 10 patients shows up with a certain medical condition during each day shift (8 hours). Let P = the number of patients with the condition who show up during 1 hour of the day shift. What distribution does P follow? If it follows a known distribution, construct the PDF for P. What is the probability that 3 or fewer patients show up? What is the probability that more than 3 show up? Problem 3 What is the probability that on a particular day (during one 8 hour day shift), the researcher has no participants with asthma, and less than 8 patients with the condition show up at the hospital?
Supreeta N.
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