2. For the case of a thin copper wire, suppose that the number of flaws follows a Poisson distributionwith a mean of 2.5 flaws per millimeter.a. Determine the probability of exactly 2 flaws in a millimeter of wire.b. Determine the probability of at most 2 flaws in a millimeter of wire.C.Determine of at least 1 flaw in 2 millimeters of wire.

Given: Let the number of flaws be X X follows Poisson distribution Mean, λ = 2.5 per millimeter…

Answered: 2. For the case of a thin copper wire,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that the speed at which cars go on the freeway is normally distributed with mean 67 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car.a. What is the distribution of X? X ~ N( ? , ? )b. If one car is randomly chosen, find the probability that it is traveling more than 65 mph. Round to 4 decumal places. ?c. If one of the cars is randomly chosen, find the probability that it is traveling between 69 and 74 mph. Round to 4 decimal places. ?
An elevator has a placard stating that the maximum capacity is 3600 lb-25 passengers. So, 25 adult male passengers can have a mean weight of up to 3600/25= 144 pounds. Assume that weights of males are normally distributed with a mean of 178 lb and a standard deviation of 26 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 144 lb. b. Find the probability that a sample of 25 randomly selected adult males has a mean weight greater than 144 lb. c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 144 lb is (Round to four decimal places as needed.)
An elevator has a placard stating that the maximum capacity is 4400 lb-29 passengers. So, 29 adult male passengers can have a mean weight of up to 4400/29 = 152 pounds. Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 29 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 152 lb. b. Find the probability that a sample of 29 randomly selected adult males has a mean weight greater than 152 lb. c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 152 lb is ☐ (Round to four decimal places as needed.)
2. Doctors volunteer their time on a daily basis in a clinic. The total number of patients served in a day at the clinic has mean 90 and variance 1890. Determine the probability that 120 or more patients can be served in a day at the clinic. Use the Central Limit Theorem with continuity correction. Use linear interpolation with the normal distribution to find the probability.
Please
4. Suppose that 60% of college students own a smart phone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here?
An elevator has a placard stating that the maximum capacity is 3800 lb—26 passengers. So, 26 adult male passengers can have a mean weight of up to 3800/26=146 pounds. Assume that weights of males are normally distributed with a mean of 185 lb and a standard deviation of 39 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 146 lb. b. Find the probability that a sample of 26 randomly selected adult males has a mean weight greater than 146 lb. c. What do you conclude about the safety of this elevator?
45. Suppöse the average height of NBA players is normally distributed with mean 200cm and standard deviation 8.89cm. What is the probabilíty that a randomly selected players will have a height between 190cm and 210cm? M= 200 a. 0.7288 b. 0.7372 8=8.89 C. 0.1314 d. 0.7698 e. 0.8686
5. The mean birth weight for babies born one month early is 2630 grams. Assume that the population has a standard deviation of 220 grams. Sketch the distribution of birth weights (in grams) of children born one month early. Calculate probability of a child born one month early with a birth weight between 2100 grams and 2900 grams. Find the weight which corresponds to the top 25% of birth weights for babies born one month early.
Suppose that the speed at which cars go on the freeway is normally distributed with mean 76 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car.a. What is the distribution of X? X ~ N( ? , ? )b. If one car is randomly chosen, find the probability that it is traveling more than 74 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 79 and 85 mph. Round to 4 decimal places.
3. The taxi and takeoff time for commercial jets is a random variable x with a mean of 8 minutes and a standard deviation of 3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. a). Find the probability that for 36 jets the average taxi and takeoff time is less than 8.33 minutes per plane. b). Find the probability that for 36 jets the average taxi and takeoff times is more than 8.55 minutes.

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