You are interested in finding out the mean number of customers entering a 24-hour convenience store every 10-minutes. You suspect this can bemodeled by the Poisson distribution with a a mean of λ = 4.77 customers. You are to randomly pick n = 74 10-minute time frames, and observethe number of customers who enter the convenience store in each. After which, you are to average the 74 counts you have. That is, compute thevalue of X.(a) What can you expect the value of ✗ to be?Enter your answer using all the decimals you can.(b) Find the value of the standard deviation of X. Enter your answer using all the decimals you can.σχ(c) Find the probability that mean of the sample of 74 is between 1.6 and 4.9. If rounding only round once, at the end do not round before that.Ensure you use at least four decimals in your z-values.P(1.6 ≤ X ≤ 4.9)=☐Use at least four decimals in your answer.(d) 92% of the time, the observed value of X will exceed what value?(use at least four decimals in your answer)

Given:λ=4.77n=74 (a) The expected value of X̄ is equal to λ=4.77Answer: 4.77 (b) The standard…

Answered: You are interested in finding out the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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4.4 give the probability data analysis, show solution.
b. The lifetime X of a particular species is assumed to be exponentially distributed with mean 75 time units. Find the probability that a member of this particular species picked at random survives: i. more than 90 time units; less than 70 time units; between 70 and 85 time units. ii. iii. iv. Calculate Var(X).
The number of pedestrians using a busy crosswalk can be modeled by a Poisson distribution with A = 56.1746 pedestrians per hour. Suppose you randomly pick 53 different one-hour time frames during which you observe the crosswalk, Let X be the number of pedestrians you observe in each of these 53 times frames. Use this information to answer the following questions. a. Describe the distribution of X and the distribution of the sample mean X. Round all values to at least five decimals if necessary The distribution of X is ? vwith a mean uy of pedestrians and a standard deviation ox of pedestrians. The distribution of X is ? v with a mean x of pedestrians and a standard deviation o, of pedestrians. b. What is the probability that the average number of pedestrians using the crosswalk per hour in this sample will be between 54.2 and 57.24? Answer: Round to at least five decimals if necessary c. What is the probability that the number of pedestrians using the crosswalk in a single one-hour…
Suppose that the number of traffic accident claims received in a month is modeled by Poisson distribution with intensity λ = 4. Assume that each traffic accident claim takes values $150, $300 or $450 equally likely. Calculate the probability that the total traffic accident claim amounts to exactly $1500.
The type of battery in Jim's laptop has a lifetime (in years) which follows a Weibull distribution with parameters a = 2 and B = 4. The type of battery in Jim's tablet has a lifetime (in years) which follows an exponential distribution with parameter A = 1/4. Find the probability that the lifetime of his laptop battery is less than 2.5 years and that the lifetime of his tablet battery is less than 3.2 years. (Answer as a decimal number, and round to 3 decimal places).
A researcher collects data from 65 people to see if there is a relation between anxiety and memory in high school students. The researcher finds the following descriptive statistics: Xbar= 25.5, sX = 4.3, Ybar = 15.6, sY = 3.2, SSX = 198.4, SSY = 1152.3, and SP = 220.4. Test for a significant relation at α =0.05.
Now suppose that the manufacturing company specializing in semiconductor chips follows a Poisson distribution with an average output of 10,000 chips per day. Approximate the expected number of days in a year that the company produces more than 10,200 chips in one day. It is requested that:to. State the solution with the original formula of the distribution, explaining why you consider that distribution to be and explaining in detail what I did (do not solve the equation)b. Solve the exercise by performing the respective normal approximation, explaining step by step how and why you do it
A researcher is interested in hamster wheel-running activity during the summer versus the winter. She suspects that either the hamsters will run less during the winter to conserve energy or they will run more to keep warm. She records the activity of n = 25 hamsters during June, July, and August and compares their running-wheel revolutions per hour to the activity of the same hamsters during December, January, and February. The data are collected, and the results show an average difference score of MD - 5.7 and a sum of squares of SS = 2,851.44. What is the sample standard deviation (s) for the D scores? (one decimal)
Historically it has been observed that patients admitted to a certain hospital for treatment of influenza spend a MEAN length of 4.4 days in the hospital. Every flu season, different strains of the flu circulate: Some years the primary strain causes more severe illness (and presumably longer than average hospital stays) and other years less so (meaning presumably shorter than average stays). We assume the hospital stays are NORMALLY distributed. a. A hospital wants to see how this year's flu season compares to previous years. Therefore, state the null and alternate hypotheses that would be used to test whether the hospital is seeing a mean hospital stay that is significantly DIFFERENT than the historical mean of 4.4 days. b. FIFTEEN patients admitted for influenza treatment are then randomly sampled and the length of their hospital stay in days is given below. 4641056443743774 SAMPLE MEAN =? SAMPLE STANDARD DEVIATION =? c. Using the results of part (b), determine what type of test is…
Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. A research veterinarian at a major university has developed a new vaccine to protect horses from West Nile virus. An important question is: How predictable is the buildup of antibodies in the horse's blood after the vaccination is given? A large random sample of horses were given the vaccination. The average antibody buildup factor (as determined from blood samples) was measured each week after the vaccination for 8 weeks. Results are shown in the following time series. Original Time Series Week Buildup Factor 2 3 4…

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