A manufacturing plant produces a product whose mass follows a normal distribution with mean of 3.5 kgand a standard deviation of 0.6 kg.a) What is the probability that one such product pulled at random has a mass greater than 2.5 kg?P(x > 2.5) =b) What is the probability that one such product pulled at random has a mass less than 3.0 kg?P(x < 3.0) =

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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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Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.1 kg and a standard deviation of o=4.9 kg. Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.) -C
A random variable X has density 3x2 for 0 < x < 1. Find its variance.(use a decimal number, rounded to the nearest 1,000th. For example, 0.123)
Weights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.
Assume that females have pulse rates that are normally distributed with a mean of u=75,0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below. ne a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute. ent The probability is (Round to four decimal places as needed.) b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 78 beats per minute. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? O A. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. O B. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size. OC. Since the distribution is of sample means, not individuals,…
Exercise 5.4 A lot of 75 washers contains 5 defectives whose variability in thickness is unacceptably large. A sample of 10 washers is selected at random without replacement. 1. Determine the probability mass function of the number of defective washers (X) in the sample. 2. Find the probability that at least one unacceptable washer is in the sample. 3. Calculate the mean and variance of X.
Let the weights of 1 kg tea boxes filled with an automatic machine have a normal distribution with a mean of μ=1.03 and a standard deviation of σ=0.02 kg.a) What is the probability that any tea box will weigh less than 1 kg?b) What is the probability that any tea box will weigh higher than 1,06 kg?
A variable of two populations has a mean of 49 and a standard deviation of 14 for one of the populations and a mean of 54 and a standard deviation of 15 for the other population. a) For independent samples of sizes 34 and 45, respectively, find the mean and standard deviation of ₁ - 2. mean: standard deviation: b) Can you conclude that the variable 1 T2 is approximately normally distributed? (Answer yes or no) answer:
Assume two normal distributions where μ1 = 0.0001, σ1 = 0.01, μ2 = -.0002, σ2 = 0.015, and ρ = .45. Using zs = { .814, .259 }, generate z1 and z2.
Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.1 kg and a standard deviation of o= 5.6 kg. Complete parts (a) through (c) below. ... a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.)
The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630
Please answer both parts of the question thanks
Question 7 According to the data, the weight of a randomly selected checked-in luggage has a normal distribution with a mean of 51 lbs and a standard deviation of 9 lbs. Let X be the weight of a randomly selected checked-in luggage and let S be the total weight of a random sample of size 33. 1. Describe the probability distribution of X and state its parameters and o: X~ Select an answer (μ = Select an answer unknown X² B N T 2. Use the Central Limit Theorem and find the probability that the weight of a randomly selected checked-in luggage is less than 61 lbs. (Round the answer to 4 decimal places) Check-In Select an answer Select an answer the original population is normally distributed the sample size is large (n>30) although the distribution of the original population is unknown the sample size is small (n<30) and the distribution of the original population is unknown the distribution of the original population is unknown S~ Select an answer (s= Select an answer σ= to describe the…

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manufacturing plant produces a product whose mass follows a normal distribution w and a standard deviation of 0.6 kg. ) What is the probability that one such product pulled at random has a mass greater P(x>2.5) = D) What is the probability that one such product pulled at random has a mass less tha