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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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
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
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.
3) Suppose test scores are measured by the Gaussian Normal Distribution N(X,75,10) calculate the following. a) Pr(80 < X < 90) b) Pr(50 < X < 70) c) The 95 th percentile
47. Let X have a Nonstandard Normal Distribution with µ = 55 and o = 8. Find P(X < 59). A. 0.68146 В. 0.69146 С. 0.70146 D. 0.71146

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