A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund hasover 125 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has meanH = 1.2% and standard deviation o = 1.3%.n USE SALT(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of allEuropean stocks. Is it reasonable to assume that x (the average monthly return on the 125 stocks in the fund) has adistribution that is approximately normal? Explain.Yes, x is a mean of a sample of n = 125 stocks. By the central limit theorem o, the xdistribution isapproximately normal.(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%?(Round your answer to four decimal places.)(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%?(Round your answer to four decimal places.)(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Whywould this happen?O Yes, probability increases as the standard deviation increases.O Yes, probability increases as the mean increases.O No, the probability stayed the same.Yes, probability increases as the standard deviation decreases.(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake yourconfidence in the statement that u = 1.2%? If this happened, do you think the European stock market might be heatingup? (Round your answer to four decimal places.)P(x > 2%) =

Answered: A European growth mutual fund…

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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A certain mutual fund invests in both U.S. and foreign markets. Let x a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.3%. (a) The fund has over 175 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 175 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2. The random variable -Select-v is a mean of a sample size n = 175. By the -Select- v, the -Select- distribution is approximately normal. (b) After 6 months, what is the probability that thẹ average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has…
The number of earthquakes per day in the world has a Poisson distribution with parameter ?= 55. Suppose that the random variable X is the number of earthquakes occurring in one day in the world. Let the random variable Y be the total number earthquakes occurring in the world in 3 days. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.a. For our model, what is expected value of X? b. What is the probability that X = 55? c. What is the probability that X > 55? d. What is the probability that X >60? e. What is the smallest value C so that there is at least a 0.9 probability of no more than C earthquakes in a day? f. Y also has a Poisson distribution. What is the parameter ?y for Y? g. What is the standard deviation of X? h. What is the probability Y =164? i. What is the probability that Y < 164? j. What is the probability that X>60 given that X>55?
The average speeds of cars on a highway are distributed according to a normal distribution. Today, John is on his way to work. As he enters the highway, he notices a car speeding by at 150 km/hr. Ten seconds later, another car speeds by at 160 km/hr. John concludes that today, cars must be going faster for some reason. A few minutes later, John gets into a minor accident. Once again, he concludes that it was inevitable - he got into the accident because cars were driving faster today. Explain what fallacies - if any-are involved in both of John's claims. Is John justified in his conclusions?
True or False
4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min
In a large city, researchers selected a random sample of 120 individuals who have multiple televisions in their house connected to a streaming device. Each individual was asked how many hours of streaming content they watch in a typical week. The sample had a mean of 12.5 hours. For which of the following populations is 12.5 hours a reasonable estimate of the mean hours of weekly streaming content watched? (A) All individuals who regularly watch streaming content (B) All individuals from this city who regularly watch streaming content (C) All individuals from this city with multiple streaming devices in their house (D) All individuals from this city with multiple streaming devices in their house who regularly watch streaming content (E) All 120 individuals in this city with multiple streaming devices in their home who regularly watch streaming content
34) If a population exhibits a skew of -5.00 and an excess kurtosis of 5.00 which of the following is true? The population mean exceeds the median. The population variance exceeds the standard deviation. The population standard deviation exceeds the variance. The population median equals the mean. The population median exceeds the mean.
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
I just need help with (d) and (e)
Suppose that we have disjoint normal populations A and B with equal but unknown population variances. Suppose we plan a sample of size 12 from from population A and a sample of size 6 from population B which we will pool to form the pooled variance. If the sample variance for the sample from population A is 25 and the sample variance for the sample from population B is 36, then what is the pooled sample variance?
Historically it has been observed that patients admitted to a certain hospital for treatment of influenza spend a MEAN length of 4.4 days in the hospital. Every flu season, different strains of the flu circulate: Some years the primary strain causes more severe illness (and presumably longer than average hospital stays) and other years less so (meaning presumably shorter than average stays). We assume the hospital stays are NORMALLY distributed. a. A hospital wants to see how this year's flu season compares to previous years. Therefore, state the null and alternate hypotheses that would be used to test whether the hospital is seeing a mean hospital stay that is significantly DIFFERENT than the historical mean of 4.4 days. b. FIFTEEN patients admitted for influenza treatment are then randomly sampled and the length of their hospital stay in days is given below. 4641056443743774 SAMPLE MEAN =? SAMPLE STANDARD DEVIATION =? c. Using the results of part (b), determine what type of test is…
A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 325 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.5% and standard deviation σ = 0.9%.A button hyperlink to the SALT program that reads: Use SALT.(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 325 stocks in the fund) has a distribution that is approximately normal? Explain. Yes, x is a mean of a sample of n = 325 stocks. By the central limit theorem, the x distribution is approximately normal. (b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.) (c) After 18 months, what is the probability that the average monthly…

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