Answered: Calculate the percentage of hours in…

Math

Statistics

Calculate the percentage of hours in which less than 2 customers enter the shop.

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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1. If X - N(200,2²), find а) Р(X < 197) b) Р(X < 200.5) 2. Let x be a continuous random variable that is normally distributed with a mean of 80 and a standard deviation of 12. Find the probability that x assumes a value a. greater than 69 c. greater than 101 b. less than 73 d. less than 87 3. Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value a. between 29 and 36 b. between 22 and 35 4. Let X denote the time taken to run a road race. X is normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race a. in less than 160 minutes? b. in 215 to 245 minutes?
6. A kinesiologist wanted to examine the effects of temperature and humidity on exercise performance. Each participant was asked to walk on a treadmill at a normal pace for 60 minutes, and the kinesiologist recorded the distance walked (miles). She assigned participants to one of 4 conditions that varied in temperature (normal or high) and humidity (normal or high). Mean distance walked by the four groups are shown in the table below. Assume a = .05 and Tukey HSD = 0.39. Normal temperature High temperature Normal humidity M = 3.00 M = 2.80 High humidity M = 2.80 M = 2.00 Complete the following conclusion: The factorial ANOVA revealed significant main effects of temperature [F (1, 24) = 25.00, p<.05] and humidity [F (1, 24) = 19.65, p<.05] and a significant Temperature x Humidity interaction [F (1, 24) = 9.25, p < .05].
(b) Predict what will happen to the data distribution if outlier exists in the data.
6. Consider a coffee shop that uses a single-server queue. The inter-arrival time is exponentially distributed with a mean of 10 minutes and the service time is also exponentially distributed with a mean of 8 minutes. Calculate the: (i) mean wait in the queue (2) (ii) mean number in the queue (2) (iii) the mean wait in the system (2) (iv) mean number in the system (2) (v) proportion of time the server is idle. (2) [10] 7. The arrival of customers at a bank follows a Poisson distribution with a mean arrival rate of 10 customers per hour. The service time at the bank follows an exponential distribution with a mean service rate of 6 minutes per customer. Calculate the average number of customers in the system (including those being served and waiting) and the average time a customer spends in the system. How is the system performing? [8]
4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st
2. It is known that the student score data in a class is as follows: 9, 8, 6, 7, 7, 8, 5, 3, 6, 7 Describe the data in terms of central tendency!
5. The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. Find the probability that the percent of fat calories a person consumes is more than 40. Sketch the associated graph/figure. Find the maximum number for the lower quarter of percent of fat calories. Sketch the graph, and write the probability statement (i.e. interpret calculated value).
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In a large city, researchers selected a random sample of 120 individuals who have multiple televisions in their house connected to a streaming device. Each individual was asked how many hours of streaming content they watch in a typical week. The sample had a mean of 12.5 hours. For which of the following populations is 12.5 hours a reasonable estimate of the mean hours of weekly streaming content watched? (A) All individuals who regularly watch streaming content (B) All individuals from this city who regularly watch streaming content (C) All individuals from this city with multiple streaming devices in their house (D) All individuals from this city with multiple streaming devices in their house who regularly watch streaming content (E) All 120 individuals in this city with multiple streaming devices in their home who regularly watch streaming content
From reviewing the temperature data for one of the regions of Iraq for a period of time, it was found that 15% of the days of the month of July (the number of days is 31) have a maximum temperature of more than 42 degrees Celsius and that 5% of the days of July have a temperature of less than 36 degrees Celsius. If you know that the temperature for the month of July in this region is subject to a normal distribution, then the mean and standard deviation S for this distribution are equal to:
. A process that cuts lengths of metal with high precision has historically produced metal rods with length that is normally distributed and with a mean of 800 millimetres (mm). Management at the factory is concerned that after an overhaul of the machine the mean length of the rods being produced could differ from the required 800 mm. If it is found that the rods are not being produced to specifications then the machine will have to be stopped for readjustment, with a consequent loss of production. The production line manager tasked with investigating the issue finds that a (random) sample of 25 rods yielded a mean length of 806 mm and a sample standard deviation of 10 mm. i. The mean of the sample is clearly not the required 800 mm. Say why this is not enough information in itself to say if the machine is operating correctly or not. ii. State the null and alternative hypotheses for this situation.
Give the statistical meaning of the relationship between the spending hours on using mobile andreading books per day