Suppose that the lifespan of a certain model of laptop is normally distributed with mean4 years and standard deviation 4 months. Throughout this problem, use the 68-95-99.7% Rule from your notes to solve each part, with all work shown.(a) What is the probability that a laptop will last between 3 years + 4 monthsand 4 years + 8 months?(b) What is the probability that a laptop will last between 4 years and 4 years+ 8 months?(c) What is the probability that a laptop will last less than 3 years + 4 months?(d) What is the probability that a laptop will last between 4 years + 4 monthsand 5 years?(e) Suppose you and your friend bought the same exact model of laptop at thesame time, and their laptop lasted less than 3 years + 4 months after purchase, whileyours lasted longer than 4 years + 8 months. What is the probability that this wouldoccur? That is, what is the probability that one laptop chosen at random will last atmost 3 years + 4 months, while another will last more than 4 years + 8 months?Assume that laptop lifespans are independent of each other. (Again, look at the definition of independence of r.v.s)
Suppose that the lifespan of a certain model of laptop is normally distributed with mean4 years and standard deviation 4 months. Throughout this problem, use the 68-95-99.7% Rule from your notes to solve each part, with all work shown.(a) What is the probability that a laptop will last between 3 years + 4 monthsand 4 years + 8 months?(b) What is the probability that a laptop will last between 4 years and 4 years+ 8 months?(c) What is the probability that a laptop will last less than 3 years + 4 months?(d) What is the probability that a laptop will last between 4 years + 4 monthsand 5 years?(e) Suppose you and your friend bought the same exact model of laptop at thesame time, and their laptop lasted less than 3 years + 4 months after purchase, whileyours lasted longer than 4 years + 8 months. What is the probability that this wouldoccur? That is, what is the probability that one laptop chosen at random will last atmost 3 years + 4 months, while another will last more than 4 years + 8 months?Assume that laptop lifespans are independent of each other. (Again, look at the definition of independence of r.v.s)
Suppose that the lifespan of a certain model of laptop is normally distributed with mean4 years and standard deviation 4 months. Throughout this problem, use the 68-95-99.7% Rule from your notes to solve each part, with all work shown.(a) What is the probability that a laptop will last between 3 years + 4 monthsand 4 years + 8 months?(b) What is the probability that a laptop will last between 4 years and 4 years+ 8 months?(c) What is the probability that a laptop will last less than 3 years + 4 months?(d) What is the probability that a laptop will last between 4 years + 4 monthsand 5 years?(e) Suppose you and your friend bought the same exact model of laptop at thesame time, and their laptop lasted less than 3 years + 4 months after purchase, whileyours lasted longer than 4 years + 8 months. What is the probability that this wouldoccur? That is, what is the probability that one laptop chosen at random will last atmost 3 years + 4 months, while another will last more than 4 years + 8 months?Assume that laptop lifespans are independent of each other. (Again, look at the definition of independence of r.v.s)
Suppose that the lifespan of a certain model of laptop is normally distributed with mean 4 years and standard deviation 4 months. Throughout this problem, use the 68-95- 99.7% Rule from your notes to solve each part, with all work shown. (a) What is the probability that a laptop will last between 3 years + 4 months and 4 years + 8 months? (b) What is the probability that a laptop will last between 4 years and 4 years + 8 months? (c) What is the probability that a laptop will last less than 3 years + 4 months? (d) What is the probability that a laptop will last between 4 years + 4 months and 5 years? (e) Suppose you and your friend bought the same exact model of laptop at the same time, and their laptop lasted less than 3 years + 4 months after purchase, while yours lasted longer than 4 years + 8 months. What is the probability that this would occur? That is, what is the probability that one laptop chosen at random will last at most 3 years + 4 months, while another will last more than 4 years + 8 months? Assume that laptop lifespans are independent of each other. (Again, look at the definition of independence of r.v.s)
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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