A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 375 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.2% and standard deviation σ = 0.5%.
(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 375 stocks in the fund) has a distribution that is approximately normal? Explain. , x is a mean of a sample of n = 375 stocks. By the , the x distribution 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 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? Why would this happen?
Yes, probability increases as the mean increases.
Yes, probability increases as the standard deviation decreases.
No, the probability stayed the same.
Yes, probability increases as the standard deviation increases.
(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that μ = 1.2%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)
P(x > 2%) = ?????
Explain. This is very likely if μ = 1.2%. One would suspect that the European stock market may be heating up.
This is very likely if μ = 1.2%. One would not suspect that the European stock market may be heating up.
This is very unlikely if μ = 1.2%. One would not suspect that the European stock market may be heating up.
This is very unlikely if μ = 1.2%. One would suspect that the European stock market may be heating up.
In: Math
Long answer question [5 marks]
Winnipeg district sales manager of Far End Inc. a university textbook publishing company, claims that the sales representatives makes an average of 40 calls per week on professors. Several representatives say that the estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was 42 and variance is 4.41.
Conduct an appropriate hypothesis test, at the 5% level of significance to determine if the mean number of calls per salesperson per week is more than 40.
(a) Provide
the hypothesis statement
(b) Calculate
the test statistic value
(c) Determine
the probability value
(d) Provide an interpretation of the P-value (1
Mark)
In: Statistics and Probability
The director of publications for a university is in charge of deciding how many programs to print for football games. Based on the data, the director has estimated the following probability distribution for the random variable X= number of programs sold at the university football game:
X 25,000 40,000 55,000 70,000
P(X) 0.1 0.3 0.45 0.15
a)Compute the expected number of program sold at the university football game.
b)Compute the variance of program sold at the university football game.
c) Each program cost $1.25 to print and sells for $3.25. Any programs left unsold at the end of the game are discarded. The director has decided to print ether 55,000 or 70,000. Which of these two options maximizes the expected profit from program?
In: Statistics and Probability
The director of publications for a university is in charge of deciding how many programs to print for football games. Based on the data, the director has estimated the following probability distribution for the random variable X= number of programs sold at the university football game:
X 25,000 40,000 55,000 70,000
P(X) 0.1 0.3 0.45 0.15
a)Compute the expected number of program sold at the university football game.
b)Compute the variance of program sold at the university football game.
c) Each program cost $1.25 to print and sells for $3.25. Any programs left unsold at the end of the game are discarded. The director has decided to print ether 55,000 or 70,000. Which of these two options maximizes the expected profit from program?
In: Statistics and Probability
Problem 2. Test Scores Distribution.
In a certain exam is taken by 200 students, the average score was 60 out of maximum of 100 points. It was also found that 32 students scored more than 75 points. Assuming that the exam scores were well represented by a Gaussian probability density function,
(2a) Determine the mean of the distribution.
(2b) Determine the standard deviation of the distribution.
(2c) Determine the number of students who scored more than 90 points.
(2d) Determine the number of students who scored less than 45 points.
(2e) Write down the expression for the Gaussian distribution that represents the PDF of the exam scores. Make sure that the expression contains all numerical fields filled in with the actual values.
In: Statistics and Probability
3. Fionn observed that 91% of the background checks he processes are for potential employees who have already interviewed. Let X be the number of background checks Fionn processes to get his first background check for a potential employee who has not yet interviewed for the job. Assume that the interview statuses are independent.
(a) Find the probability that the 2nd background check that Fionn processes is the first for which the potential employee has not yet interviewed.
(b) What is the underlying process for the random variable X?
A. Bernoulli Process B. Stochastic Process C. Binomial Process D. Random Process
(c) Suppose Y is the number of potential employees who have already interviewed in a group of 15 employees. How are X and Y different?
In: Statistics and Probability
Sampling Distribution. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from its Internet Project survey. One was that the average adult user of Facebook has 338 friends. This population distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a reported median of 200 friends.
Suppose that σ = 380 and you take an SRS of 80 adult Facebook users.
a. For your sample, what are the mean and standard deviation of ̅ (xbar), the mean number of friends per adult user?
b. Use the central limit theorem to find the probability that the average number of friends for 80 Facebook users is greater than 350.
In: Statistics and Probability
Please do it by type not pic.
1. The Heart Association plans t install a free blood pressure testing booth at the Palouse mall for a week. Previous experience indicates that, on average, 10 persons per hour request a test and the arrivals are Poisson distributed from an infinite population. Blood pressure measurements are exponential with an average time of 5 minutes per exam.
a. What is the average number of people in line?
b. What is the average number of people in the system?
c. What is the average amount of time a person can expect to spend in line?
d. What is the average amount of time it will take to measure a person's blood pressure, including waiting in line?
e. What is the probability of having 3 people in line ?
In: Operations Management
Students of a large university spend an average of $7 a day on lunch. The standard deviation of the expenditure is $2. A simple random sample of 25 students is taken. What is the probability that the sample mean will be at least $4? Jason spent $15 on his lunch. Explain, in terms of standard deviation, why his expenditure is not usual. Explain what information is given on a z table. For example, if a student calculated a z value of 2.77, what is the four-digit number on the z table that corresponds with that value? What exactly is that 4-digit number telling us? Explain why we use z formulas. Why don't we just leave the data alone? Why do we convert? must show work
In: Statistics and Probability
Please do it by type not pic.
1. The Heart Association plans t install a free blood pressure testing booth at the Palouse mall for a week. Previous experience indicates that, on average, 10 persons per hour request a test and the arrivals are Poisson distributed from an infinite population. Blood pressure measurements are exponential with an average time of 5 minutes per exam.
a. What is the average number of people in line?
b. What is the average number of people in the system?
c. What is the average amount of time a person can expect to spend in line?
d. What is the average amount of time it will take to measure a person's blood pressure, including waiting in line?
e. What is the probability of having 3 people in line ?
In: Operations Management