3.Let X equal the birth weight (in grams) of babies in United States. Assuming thatthe distribution of X is normal distribution with μ = 3315 and σ = 575.(a) Compute P (2584.75 ≤ X ≤ 4390.25)? (10%)(b) Let Y equal the number of babies that weight less than 2719 grams at birthamong 25 of these babies selected independently. Compute P(Y ≤4) (10%)

Given informationX = birth weight (g) of babies in the United StatesX is normally distributedμ…

Answered: 3. Let X equal the birth weight (in…

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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3. Let Y, < Y2 < Y, be the order statistics of 3 independent observations from a distribution with 20th percentile n0.2 = 5. Find P(Y, <5). %3D
8. In the UK (United Kingdom) Baby Birth weight can be approximated by a Normal Distribution with N(3.39, 0.55) with numbers being in kg (kilograms) D. Compute P(birth weight > 4 kg) using a normal distribution calculator E. Compute the Z-Score for a 2 kg birth F. Compute P(birth weight < 2 kg) using a normal distribution calculator
10. a.) Find the z-value such that 80 percent of the area under the standard normal curve lies between -z and z. b). Find the z value if the normal curve area to the right of z is 0.6449. is from N(0,1) de in a cmall town at California is 0.2 everyday, what is the
3. Find the boundary that corresponds the the probability for the standard normal distribution. (a) P(z< zo) = 0.8203 (b) P(zo < z) = 0.8997 4. Find the boundary that corresponds the the probability for the normal distribution. (a) P(x < xo) = 0.8203 when µ„ = 25 and op = 6.5 (b) P(yo < y) = 0.8997 when ly = 25 and oy = 6.5
A Normal distribution has mean =28 and a standard deviation =5. A) find the z score corresponding to x =23. B) find the z score corresponding to x =39 C) find the raw score corresponding to z = -2 D) find the raw score corresponding to z = 1.7
time, i.e. P(μx-ox ≤ x ≤ μx + 0x). 3. Suppose that people heights are normally distributed with mean of 170 cm and standard deviation of 6 cm. a) What proportion of people are between 165 cm and 175 cm tall? b) Find the minimum ceiling of an airplane such that at most 5% of people walking down the aisle will have to duck. E c) Find the probability that the average height of a random sample of 49 people is greater than 172 cm. 80 F3 4 R % 5 T F6 Y 1 & 7 K ard deviation of the expected U 8 DII
5. The distribution of male weight in the United States has a standard deviation of roughly o = 25 lbs. The average weight u varies from state to state. Suppose you randomly select 100 males in Louisiana and ask their weights, and you compute the average weight Xn of the n = 100 males. a) Assuming that the standard deviation of weight in Louisiana is 25 lbs, what does the Central Limit Theorem tell you the (approximate) distribution of X will be?
The pressure of air (in MPa) entering a compressor is measured to be X = 8.5 ± 0.2, and the pressure of the air leaving the compressor is measured to be Y = 21.2 ± 0.3. The intermediate pressure is therefore measured to be P = √XY = 13.42 . Assume that X and Y come from normal populations and are unbiased. a) From what distributions is it appropriate to simulate values X* and Y*? b) Generate simulated samples of values X*, Y*, and P*. c) Use the simulated sample to estimate the standard deviation of P. d) Construct a normal probability plot for the values P*. Is it reasonable to assume that P is approximately normally distributed? e) If appropriate, use the normal curve to find a 95% confidence interval for the intermediate pressure.
33. If X is a normal variate with mean u and variance X- o? and P - b< .2
Consider a normal distribution curve where 70-th percentile is at 12 and the 45-th percentile is at 7. Use this information to find the mean, μ, and the standard deviation, o, of the distribution. a) με b) σ =
33. Let X have a Nonstandard Normal Distribution with u = 55 and o = 8. Find P(X < 59). C. 0.70146 A. 0.68146 B. 0.69146 D. 0.71146
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

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