Question 1It is known that if a signal of value is sent from location A, thenthe value received at location B is normally distributed with meanμ and standard deviation 2. That is, the random noise added to thesignal is an N(0,4) random variable. There is reason for the peopleat location B to suspect that the signal value = 8 will be senttoday.a) What test statistics will be needed to measure the accuracy of theconjecture about the average value of signal received. b) Test this hypothesis if the same signal value is independently sentfive times and the average value received at location B is * = 9.5.suppose we test at 5% level.

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Answered: It is known that if a signal of value…

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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Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. (a) In words, define the random variable X. Edit Insert Formats BIUX₂ + 2+ 3 = C P & (b) Find the z-score for a trial lasting 19 days. your answer to three decimal places.) Shade: Left of a value (c) If one of the trials is randomly chosen, find the probability that it lasted at least 19 days. +||||||||| (d) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (b), rounded to one decimal place). -1 X² A ▾ A▾ -1.5 用 Σ+ Σ Α 2 Click and drag the arrows to adjust the values. (Round ++++++++++++ 3 4 (e) eighty-eight percent of all trials of this type are completed within how many days?
According to the Center for Disease Control, the mean total cholesterol for men between the ages of 20-29 is 180 milligrams per deciliter with a standard deviation of 36.2. A healthy total cholesterol level is less than 200,200-240 is borderline and above 240 is dangerous. Assume the distribution is approximate. if two randomly selected men are chosen from this group, what is the probability that both will have a total cholesterol level of 200 or more? assume independence.
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It is known that the mean weight of students at cavendish university is 72 kg with a standard deviation of 3 kg. What would be the probability of finding individuals with weights between 74kg and 78 kg? ( Assume weight to be normally distributed).
It is known that the average body temperature of healthy individuals is is normally distributed with a mean, μ = 37 oC and standard deviation, σ = 0.6 oC. We found the average temperature of a random sample of 24 University students in a Statistics tutorial. What is the probability that the average body temperature of this sample of students will be less than 37.1 oC? (4 dp) What is the probability that average body temperature of these students will be more than 37.4 oC?
It is known that the mean blood pressure of a community is 125 mm of Hg with a standard deviation of 3 mm of Hg. What would be the probability of finding individuals with blood pressure less than 120 mm of Hg in the community? ( Assume blood pressure is normally distributed).
It is known that the mean weight of student at Cavendish University is 72 kg with a standard deviation of 5 kg. What would be the probability of finding individuals with weights less than 705 kg? ( Assume weight to be normally distributed)
If the distribution of the population has a nonzero standard deviation and mean 12 then the probability that an individual data value will be greater than 14 is always less than the probability that the mean of 45 randomly selected data values will be greater than 14. True or False
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0 degrees * C and a standard deviation of 1.00 degrees * C . A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than - 1.388 degrees * C . If this can be done on the calculator, please explain.
The distribution of heights of a certain breed of terrier has a mean of 71 centimeters and a standard deviation of 9 centimeters, whereas the distribution of heights of a certain breed of poodle has a mean of 29 centimeters with a standard deviation of 5 centimeters. Assuming that the sample means can be measured to any degree of accuracy, find the probability that the sample mean for a random sample of heights of 64 terriers exceeds the sample mean for a random sample of heights of 100 poodles by at most 44.2 centimeters. What is the probability? Round to four decimals. Use standard normal distribution table.
Suppose a manufacturer produces light bulbs and claims that their average lifespan is 1000 hours with a standard deviation of 100 hours. If a random sample of 50 light bulbs is taken, what is the probability that the average lifespan of the sample will be greater than 1050 hours? And how does this probability change if the sample size is increased to 100?
A psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes each day until they give birth. After 5 years, the child is administered an 1Q test. It is known that IQs are normally distributed with a mean of 100. If the IQs of the 20 children in the study result in a sample mean of 104.4 and sample standard deviation of 16, is there evidence that the children have higher IQs? Use the a= 0.10 level of significance. Complete parts (a) through (d). (a) Determine the null and alternative hypotheses. Ho: H = 100 Hy: H > 100 (b) Calculate the P-value. P-value = (Round to three decimal places as needed.) %3D Enter your answer in the answer box and then click Check Answer. 2 parts remaining Clear All Check Answer 80 888 112 F7 esc F4 F2 & @ %23 delete 7 8 9 2 3 4 { Q W E Y tab F G H K A D caps lock V B N M C - - .. .- つくC N

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