STAT6315_Homework3Solutions

6 a randomly selected value from a normal

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Unformatted text preview: increased). 6. A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean. a) What is the probability that a randomly selected value from the distribution will be greater than 2.1 standard deviations above the mean? Page 4 of 8 b) What is the probability that a randomly selected value from the distribution will be less than 2.1 standard deviations from the mean? | | 7. Assume that a random variable is normally distributed with a mean of 1,500 and a variance of 324. a) What is the probability that a randomly selected value will be greater than 1,550? ( √ ) 0027 b) What is the probability that a randomly selected value will be less than 1,485? ( ) 2033 c) What is the probability that a randomly selected value will be either less than 1,475 or greater than 1,535? ( ) Page 5 of 8 ( ) 8. A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selected from the distribution, a) What value will be exceeded 10% of the time? b) What value will be exceeded 85% of the time? c) Determine the first and third quartiles of the distribution. d) What value will 15% of the observations be below? Page 6 of 8 9. An internet retailer stocks a popular electronic toy at a central warehouse that supplies the eastern United States. Every week the retailer makes a decision about how many units of the toy to stock. Suppose that weekly demand for the toy is approximately normally distributed with a mean of 2,500 units and a standard deviation of 300 unites. a) If the retailer wants to limit the probability of being out of stock of the electronic toy to no more than 2.5%...
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