**Example 3.7.9**Suppose that a healthcare provider selects 20 patients randomly (without replacement) from among 500 to evaluate adherence to a medication schedule. Suppose that 10% of the 500 patients fail to adhere to the schedule. Determine the following:a. Probability that exactly 10% of the patients in the sample fail to adhere.

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Answered: 3.7.9 SS Suppose that a healthcare…

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.A personnel manager is employed in a corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.Find the 95th percentile for the mean time to complete one month's reviews. (a) Sketch the graph.(b) Give the 95th Percentile. (Round your answer to two decimal places.)
5. The meat department at a local supermarket specifically prepares its "1-pound" packages of ground beef so that there will be a variety of weights, some slightly more and some slightly less than 1 pound. Suppose that the weights of these "1-pound" packages are normally distributed with a standard deviation of 0.15 pound. What is the probability that a randomly selected package of ground beef will weigh less than 0.80 pound?a. 0.2088b. 0.9088c. 0.0918d. 0.4088
5) The daily revenue at a university snack bar has records to indicate that the mean daily revenue is $2,400 and standard deviation is $600. A random sample of 81 days was selected. Find the approximate probability that the average revenue for the sample is less than $2,300.
A survey was conducted to measure the number of hours adults spend sleeping each week. In the survey, the number of hours was normally distributed, with an average of 7 hours and a standard deviation of 1 hour. One adult was chosen at random. Which of the alternatives below corresponds to the probability that this participant will spend more than 10 hours a week sleeping? a) 0,9987% b) 13% c) 99,87% d) 0,13%
3. The amount of time it takes a TELNOR cashier to serve customers in service by car is a normally distributed random variable, with mean 3.2 minutes and standard deviation 1.6 minutes. Given a random sample of 64 customers served in a day, find the probability that the average time spent serving these customers is: (a) less than 2.7 minutes b) more than 3.5 minutes c) at least 3.0 minutes, but less than 3.4 minutes.
. Each member of a large genetics class grows 12 pea plants from an independent pea family. Each family is expected to have 3/4 plants with smooth peas and 1/4 plants with wrinkled peas. a. On average, how many wrinkled pea plants will a student see in her 12 plants? b. What is the standard deviation of the proportion of wrinkled pea plants per student? c. What is the variance of the proportion of wrinkled pea plants per student? d. Predict what proportion of the students saw exactly two wrinkled pea plants in their sample.
12. The life span of an automatic washer X is normally distributed random variable with the mean of 3.8 years and standard deviation of 1.2 years. a. Probability that life span of randomly selected washer will be more than 3.5 years is b. The percent of the washers with the life span between 3.5 years and 4.0 years is c. The dealer wants only 1.5% of the washers to fail before the end of guarantee period. Then the length of guarantee period is years. Show your work in finding probability (percent) in the questions a, b, and answering the question c.
Suppose the demand for a company’s product in week 1,2, & 3 are each normally distributed. The means are 50, 45, and 65. The standard deviations are 10,5, and 15. Assume these 3 demands are probabilistically independent. Suppose the company has 180 units in stock, and it will not be receiving any more shipments from its supplier for at least 3 weeks. What is the probability that stock will run out during the 3 week period? How many units should the company have in stock, so that it can be 98% certain of not running out during the 3 week period , assuming it will not receive any more shipments during this period?
. The demand for high-grade gasoline at a service station is normally distributed with mean 27,009 gallons per day and standard deviation 4,530. Find two values that will give a symmetric 0.98 probability interval for the amount of high-grade gasoline demanded daily.
a) Calculate the standard deviation of the following estimated probability distribution of hurricane evacuation time: Time to Evacuate nearest hour Probability 13 0.04 14 0.25 15 0.40 16 0.18 17 0.10 18 0.03 b) Phone call arrive at the rate of 48 per hour at the reservation desk for Regional airways. Calculate the probability of receiving three calls in a five-minute interval of time. c) A university has found that 20% of its students withdraw without completing introductory calculus course. 20 students have registered for the course this quarter. Calculate the following: i) Probability that two or fewer will withdraw. ii) Mean of withdrawals.
6.2) The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $12. Find the probability that a randomly selected utility bill is a) less than $70 b) between $90 and $120 c) more than $140
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.6 days and a standard deviation of 2.3 days. 1.) What is the probability of spending more than two days in recovery? A.)0.8709 B.) 0.0495 C.) 0.9412 D.) 0.0588 2.) The 80th percentile for recovery times is? A.) 7.54 B.) 4.24 C.) 7.01 D.) 6.81

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