5) Normal DistributionA soft drink machine is calibrated to dispense an average of 200 milliliters (mL) per cup. Theamount of beverage dispensed is normally distributed with a standard deviation of 10 mL.a) What is the probability that a random cup will contain exactly 200 mL? e) The manufacturers want to advertise the accuracy of their soft drink machines. They wantto claim that 90% of cups will contain 200 + d mL of soft drink. What is d?f) The machine is installed in a fast-food restaurant where employees wear roller-skates tobring food to customers' cars. A new employee isn't very comfortable on roller-skates yetand spills 40% of the drinks she carries. If she delivers 100 drinks to customers on a randomday, what is the probability she spills fewer than 30 of them? Solve using the normalapproximation to the binomial distribution.

Given that:The random variable is normally distributed withmean milliliters(mL) per cup,Standard…

Answered: 5) Normal Distribution A soft drink…

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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For a statistic to be a good estimator of a parameter, two properties it must satisfy are unbiasedness and minimum variance. Consider a sample of three observations X₁, X₂, X, where X, ~ Exp (0). That is, a sample of size 3 is taken from a population 2 3 following the exponential distribution with density function given by f(x) = 1e % if x > 0 0, Otherwise. Five possible estimators of are â‚ =X₁, Ô₂ = ¹/(X₁ + X₂), Ô‚ = =— (X₁ + 2X₂), Ô¸ = X, and Ô¸ = ¹⁄ (X₂ + X). 2 [Hint: Use the fact that for variable X we have E(X)= 0 and E(X²)=20² and Var(X) = 0². (a) Show that the five estimators given above are unbiased for 0. (b) Find the variances of each of the five estimators. (c) Which estimator will you choose for 0. Why?
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Blood Pressure For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1 (based on data from the National Health Survey) a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is above 120. b. If 12 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 120. c. Given that part (b) involves a sample size that is not larger than 30, why can the central limit theorem be used?
Mileage data of new model cars follow a normal distribution with an average mileage of 26 mpg and a standard deviation of 7. Consider a sample of size 15 cars. What is the probability that the mean mileage of these selected cars is at most 27.5 mpg?
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 53 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean u = 53 tons and standard deviation o = 1.3 ton. n USE SALT (a) What is the probability that one car chosen at random will have less than 52.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 42 cars chosen at random will have a mean load weight x of less than 52.5 tons of coal? (Round your answer to four decimal places.)
The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm. Find the probability that an individual distance is greater than 209.30 cm.
c. Vehicle speeds at a highway location have a normal distribution with mean u = 65 mph and standard deviation o = 5 mph. Find the probability that a randomly selected vehicle speed is greater than 73 mph.
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 53 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean u = 53 tons and standard deviation = 0.9 ton. USE SALT (a) What is the probability that one car chosen at random will have less than 52.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 29 cars chosen at random will have a mean load weight x of less than 52.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 52.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? OYes O No Suppose the weight of coal in 29 cars selected at random had an average x of less than 52.5 tons. Would that fact • make you suspect that the loader had slipped out of adjustment? Why? O Yes, the probability that…
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III. SAMPLING AND SAMPLING DISTRIBUTIONS Assume that the systolic blood pressure of 30-year-old males is normally distributed, with an average of 122 mmHg and a standard deviation of 10 mmHg. а. b. Calculate the probability that the blood pressure of an individual male from this population will be between 118 and 124 mmHg.
I. NORMAL PROBABILITY DISTRIBUTION Cars are passing through a checkpoint. Assume the speeds are normally distributed such that the mean (u) = 61 mph and the standard deviation (sigma) = 4 mph. а. b. Calculate the probability (area under the curve) that the next car to pass will be travelling more than 58 mph.

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5) Normal Distribution A soft drink machine is calibrated to dispense an average of 200 milliliters (mL) per cup. The amount of beverage dispensed is normally distributed with a standard deviation of 10 mL. a) What is the probability that a random cup will contain exactly 200 mL?