4.2.8.JLet A denote the mean of a random sample of size n from a distribution that has mean u and variance o? 10. Find n so that the probability is approximately 0.954 that the random interval (X - , X+) includes u.
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- The fracture strength of bi-tempered glass averages 14.03 (measured in thousands of pounds per square inch) and has standard deviation 2. Suppose we randomly select 100 pieces of bi-tempered glass. Let M be the random variable representing the mean fracture strength of the 100 selected pieces. Let T be the random variable representing the sum of the fracture strengths of the 100 selected pieces. Using R and write the code outa) What theorem will let us treat T and M as approximately normal random variables? Monte Carlo TheoremLaw of Large Numbers 301 TheoremCentral Limit TheoremChebychev's TheoremConvolution Theorem b) What is the expected value of T? c) What is the standard deviation of T? d) What is the approximate probability that T is greater than 1400? e) What is the 98th percentile of the approximate distribution of T? f) What is the standard deviation of M? g) What is the approximate probability M is greater than 13.99? h) What is the variance of 93M?where appropriate. 1. Experience has shown that the seeds from a certain variety of orchid have a 75% chance of germinating when planted under normal conditions. Suppose n seeds are planted, and let X be the random variable that counts the number of seeds that germinate. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) = = (b) What is the minimum value of n so that the probability of at least five of the seeds germinating is at least 90%?An urn contains 7 black and 18 white balls. A ball is randomly drawn from the urn. Let X = 1 if a white ball is drawn and let X = -1 if a black ball is drawn. Find the following a) mean of X b) variance of X Please provide your working and round your answers to 2 decimal places
- The weights of beagles (dogs) have approximately a normal distribution with u = 17.1 pounds and a standard deviation of o = 1.8 pounds. Suppose that we randomly select n = 64 beagles and measure their weights in pounds. Let X be the random variable representing the mean weight of the selected beagles. Let Xtot be the random variable representing the total weight of the selected beagles. a) About what proportion of beagles have weights between 17 and 18 pounds? b) About what proportion of beagles have weights greater 20 pounds? c) About how many of the 64 sampled beagles have weights less than 16.5 pounds? (nearest integer) d) About how many of the sampled beagles have weights between 17 and 18 pounds? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot? g) What is the probability that 17 1100? f) Copy your R script for the above into the text box here.3. Let Y,,. , Y, be a random sample from a normal distribution with mean 30 and standard deviation 3. What is the probability the largest observation is greater than 30?Let x be a random variable that represents the weight of a lion in a certain region of Africa. Assume that x is normally distributed with a mean = 260 lbs . With standard deviation =30 lb Please include the graphs for questions A and B
- 34. Suppose that X is a random variable with MGF M(t) = (1/8)e + (1/4)e + (5/8)e. (a) What is the distribution of X? (b) What is P[X= 2]?13) For a random variable with mean=10 and standard deviation=2, (show work) a. Find the value that corresponds to z-score=-2.4. b. applying Chebeche's Rule, find value of k such that at least 60% of the measures are within k standard deviation of the mean.8) A normal random variable x has an unknown mean and the standard deviation. The probability that X exceeds 4 is 0.9772, and The probability that X exceeds 5 is 0.9332. Find u and o.
- 200 poodles 61 are left-paued left -pawed. a random sample of In a random sample ef 220 labradores 38 are Can we conclude that the difference in The tuo sample proportions of left pawed dogs is statistically significont for x= 0.05 ?level of blood glucose and diabetes are closoly related. Let x bo a random variable measured in milligrams of glucose per deciliter of od. After a 12-hour fast, th random variable x will have a distribution that is approximately normal with mean - 85 and standard deviation 5. What is the probability that for an adult after a 12-hour fast. s less than 7o, b. x is greater than 120?The lengths of home runs hit by players for the Mets have approximately a normal distribution with μ = 399 feet and a standard deviation of σ=31.16 feet. Suppose that we randomly select 81 home runs hit by players of the Mets. Let X be the random variable representing the mean length of home runs in feet and let Xtot be the random variable representing the sum of the lengths of the home runs in feet for the 81 selected home runs. d) About how many of the 81 sampled home runs have length between 400 and 420 feet? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot?
