Problem 4 | The daily revenue of an online retailer has mean 20 and variance 400. (i) Find the lowest possible upper bound on the probability that the daily revenue exceeds 80.
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- The personality variable extraversion is normally distributed in the population and has a mean of 10 and a standard deviation of 3. Researchers consider individuals who have extraversion scores greater than 13 to be "highly" extroverted. What is the probability that you can randomly sample 2 people from the population, and both would be highly extroverted?The graph of the standard deviation indicates that the tighter the probability distribution, the higher the possibility of achieving the expected return hence it is a less risky investment. Is it True or False?A bridge can resist a weight up to 104 metric tons. The mean weight of a car is 4 tons with a variance of 9 tons. On a given day, there are 2450 cars on the bridge, approximate the probability that the bridge will fail
- The Vice President of sales for the conglomerate you work for has asked you to evaluate the sales records of two of the firm’s divisions. You note that the range of monthly sales for division A over the last 2 years is Rs.50,000 and the range of division B is only Rs.30,000. You compute each division’s mean monthly sales for the same time period and discover that both divisions have a mean of Rs.110,000. Assume that is all the information you have about the division’s sales records. Would you be willing to say which of the divisions has a more consistent sales record? Why or why not?Suppose, you are running an experiment for 'x' times where the probability of success in a single experiment is 'p'. If the variance of the number of successful experiments is 'x/4' , find p.The average GPA scored by a class is 4.91 and standard deviation is 0.72. For a sample of 30 students, find the probability that they will have an average GPA more than 5.
- If we correctly summed all deviations from the mean of a distribution (without squaring those deviations), we will always obtain a sum of zero. True or False ?2) Suppose that the number of miles that a car càn run before its battery wears out is exponentially distributed with an average value of 10,000 miles. If a person desires to take a 5000-mile trip, what is the probability that he or she will be able to complete the trip without having to replace the car battery? What can be said when the distribution is not exponential?Fourty percent of the students in a class of 120 are planning to go to graduate school Find the variance of the binomial distribution.
- A test has been devised to measure a student's level of motivation during high school. The motivation scores on this test are approximatley normally distributed with a mean of 40 and a standard deviaton of 10. The higher the score the greater the motivation to do well in school. What percentage of students taking his test will score above a 50?From the data set of a class, a student taking a final exam is random variable with mean equal to 50 and variance is 25. Find an upper bound for the student probability that a student's exam score will between 40 and 60.A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 84%. If it is known that returns are normally distributed with a mean of 4.1%, what is the risk, measured by standard deviation, that this investment manager assumes in his calculation?