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Scores on a management aptitude examination are normally distributed with a mean of 72 and a standard deviation of 8. What is the lowest score that will place a manager in the top 10% (90th percentile) of the distribution? What is the highest score that will place a manager in the bottom 25% (25th percentile) of the distribution?
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The Vanguard Balanced Index Fund seeks to maintain an allocation of 60% to stocks and 40% to bonds. With low fees and a consistent investment approach, this fund ranks fourth out of 792 funds that allocate 50% to 70% to stocks (US News, March 2017). Based on historical data, the expected return and standard deviation of this fund is estimated as 7.49% and 6.41%, respectively. Assume that the fund returns are stable and are normally distributed. a) What is the probability that the fund will generate a return between 5% and 10%? b) What is the lowest return of the fund that will place it in the top 10% (90th percentile) of the distribution?
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WHAT IS THE EXPONENTIAL DISTRIBUTION?
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Let the time between e-mail messages during work hours be exponentially distributed with a mean of 25 minutes. a) Calculate the rate parameter λ. b) What is the probability that you do not get an e-mail for more than one hour? c) What is the probability that you get an e-mail within 10 minutes?
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A barbershop has an average of 12 customers between 8:00 am and 9:00 am every Saturday. Customers arrive according to the Poisson distribution. What is the probability that the time between consecutive arrivals (customers) will fall between 3 and 6 minutes?
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Define The Discrete Probability Distribution
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Consider an experiment of rolling a fair six-sided die, with the random variable X defined as the number rolled. Present the probability distribution in a tabular form.
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WRITE TWO KEY PROPERTIES OF DISCRETE PROBABILITY DISTRIBUTIONS?
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