Stock market. Give an example of a continuous random variable that would be of interest to a stockbroker.
Example: The time taken by a stockbroker for the completion of the transactions of the stocks.
The continuous random variables are those variables that take infinite values for which it is very difficult to count by anyone. The values of continuous random variables can fluctuate a lot.
The time taken for the completion of the transaction of stocks between two market participants through a stockbroker varies a lot. The variation in time depends upon the situation and the momentum of change in the stock prices, which means that it can take infinite values.
Blood diamonds. According to Global Research News (March 4, 2014), one-fourth of all rough diamonds produced in the world are blood diamonds, i.e., diamonds mined to finance war or an insurgency. (See Exercise 3.81, p. 200.) In a random sample of 700 rough diamonds purchased by a diamond buyer, let x be the number that are blood diamonds.
a. Find the mean of x.
b. Find the standard deviation of x.
c. Find the z-score for the value x = 200.
d. Find the approximate probability that the number of the 700 rough diamonds that are blood diamonds is less than or equal to 200.
The Apprentice contestants’ performance ratings. Referto the Significance (April 2015) study of contestants’ performanceson the United Kingdom’s version of the TVshow, The Apprentice, Exercise 2.9 (p. 73). Recall thatthe performance of each of 159 contestants was rated ona 20-point scale. Contestants were also divided into twogroups: those who played for a job and those who playedfor a businesspartnership. These data (simulated, based onstatistics reportedin the article) are saved in the accompanyingfile. Descriptive statistics for each of the two groupsof contestants are displayed in the accompanying Minitabprintout.
a. Determine whether the performance ratings of contestantswho played for a job are approximately normallydistributed.
b. Determine whether the performance ratings of contestantswho played for a business partnership are approximatelynormally distributed.
Descriptive Statistics: Rating
Apps not working on smartphones. In a Pew Research Center survey titled U.S. Smartphone Use in 2015, more than 2,000 smartphone users were asked how often the applications (apps) they downloaded on their cell phones were not working correctly. Responses were recorded as follows: 1 = Frequently, 2 = Occasionally, 3 = Rarely, and 4 = Never. The probability distribution for the numerical response, x, is provided in the table.
Hotels’ use of ecolabels. Refer to the Journal of Vacation Marketing (January 2016) study of travelers’ familiarity with ecolabels used by hotels, Exercise 2.64 (p. 104). Recall that adult travelers were shown a list of 6 different ecolabels, and asked, “Suppose the response is measured on a continuous scale from 10 (not familiar at all) to 50 (very familiar).” The mean and standard deviation for the Energy Star ecolabel are 44 and 1.5, respectively. Assume the distribution of the responses is approximately normally distributed.
a. Find the probability that a response to Energy Star exceeds 43.
b. Find the probability that a response to Energy Star falls between 42 and 45.
c. If you observe a response of 35 to an ecolabel, do you think it is likely that the ecolabel was Energy Star? Explain.
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