…‒‒‒‒X unknown‒‒‒According to a study, the length of pregnancy has unknown distribution with a mean of 274 days and astandard deviation of 14.8 days. Let X be the length of pregnancy for a randomly selected female and letX be the average length of pregnancy for a random sample of size 11.1. Describe the probability distribution of X and state its parametersand σ:(μ= 27✔ 0 0 ="14✓ 0)and find the probability that the length of pregnancy for a randomly selected female is more than 313days.0.0 X (Round the answer to 4 decimal places)Note: If it is not possible to compute, type "DNE"2. Explain why the Central Limit Theorem cannot be usedthe sample size is small (n<30) and the distribution of the original population is unknown00

Let X be the random variable from normal distribution with mean (μ) = 274 and standard deviation (σ)…

Answered: ling to a study, the length of…

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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-5. The weight of a certains species of fish is normally distributed with mean of 4.25 Kg and standard deviation of 1.2 a) What proportion of fish are between 3.5 kg and 4 kg b) What is the probability that a fish caught will have a weight of at least 5kg? 31
The number of people who dine at restaurants in Buffalo is normally distributed with a µ = 30 people and = 3 people. (Report both the z-scores and probability) What is the probability that the mean of 7 restaurants will have between 21 and 32 people dining there? z1 = z2 = p(21 > M > 32) = What is the probability that the mean of 13 restaurants will have less than 21 people dining there? z = p(M < 21)= Is the p=0 when the z score is extreme like -10 or 10?
1. (See Handout 1, Example 1). The life expectancy of a particular brand of lightbulb is normally distributed with a mean of 1500 hours and a standard deviation of 75 hours. We want to calculate the probability that a lightbulb will last more than 1440 hours. a) Calculate the critical z-score. b) Label the axis and shade the area under the curve that we are interested in. Hours z-score c) What is the probability that a lightbulb will last more than 1440 hours? d) What is the probability that a lightbulb will last less than 1440 hours?
The mean total cholesterol for a population of men between the ages of 20 and 29 is 180 micrograms per decilitre with a standard deviation of 37.4. A healthy total cholesterol level is less than 200, 200-240 is border line, and above 240 is dangerous. Assume the distribution is approximately Normal. For a randomly selected man from this group, what is the probability that his total cholesterol level is i. 200 or more? 1i. Between 200 and 240?
3. 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 o=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?
An elevator has a play card stating that the maximum capacity is 1980 pounds 12 passengers so 12 adult male passages can have a mean way of up to 1180÷12 = 165 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 165 lb. Assume that weights of males are normally distributed with a mean of 172 pounds and a standard deviation of 27 pounds. Does this elevator appear to be safe?
Solve using R commands and manually Suppose that blood chloride concentration (mmol/L) has a normal distribution with mean 104 andstandard deviation 5 (“Mathematical Model of Chloride Concentration in Human Blood,” J. of Med.Engr. and Tech., 2006: 25–30”).(a) What is the probability that chloride concentration equals, less than, and at most 104?(b) What is the probability that someone’s blood chloride concentration level is between 99 and 114?(c) What is the probability that someone’s blood chloride concentration level is above 120?
Q4) A capacity of a battery is normally distributed with a mean of 25.2 Kw-hr and standard deviation of 0.1 Kw-hr, find the probability that a selected battery has a capacity more than 25.11 Kw-hr 0.758 O )0.864 O 0.691 O 0.816 O
Assume that females have pulse rates that are normally distributed with a mean of μ=72.0 beats per minute and a standard deviation of σ=12.5 beats per minute. a) If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.
D = 129 , E = 56 , F = 134
Let X denote the data transfer time (ms) in a grid computing system (the time required for data transfer between a "worker" computer and a "master" computer. Suppose that X has a gamma distribution with mean value 37.5 ms and standard deviation 21.3. Round all answers to 4 decimal places and 3 = b) What is the probability that data transfer time exceeds 49 ms? a) What are the values of a = ? c) What is the probability that the data transfer time is between 49 and 67 ms?
The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 18. Suppose that 50 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. 1. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 73.9 and 76.9. 2. For the 50 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 73.9 and 76.9.

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